This is a huge question. If someone has the time to give a more thorough overview, I invite them to, but here’s a quick set of points to consider.

• Most of these end consonants are no mystery: they come directly from Latin (temps < tempus, pas < passum, roux < rossus, etc.).

• In Latin, there are regular rules for word stress, and they are rarely on the last syllable (exceptions include some inflected forms and single-syllable words).

• The end of a syllable (the coda) is among the “weak” phonological positions, where what is called lenition tends to take place. The same generally goes for a word, where the farther something is from the stress, the less loud it tends to be.

• Words thus “eroded” over time, from the end gradually back to the stressed syllable, and then to the vowel of the stressed syllable (the loudest part). What we hear in French is often the last, loudest point of the word as it existed in Latin.

• Not all consonants disappear at equal rates. Some of the most sonorant, e.g. r and l, usually are still pronounced. Some didn’t fully disappear but just became voiceless, like f < v in the suffix -if < -īvus (e.g. sportif). Others like n disappeared but only by leaving a mark in the form of a nasalized vowel where they used to be. There was also an intermediate stage where some instances of l went through a weakened u on their way out and left diphthongs that eventually turned into single, but different vowels: faux < faulx < … fals < falsus.

• In certain contexts, the final consonant is preserved. For example, je prends /pʁɑ̃/ vs. que je prenne /pʁɛn/. This is because the vowel has “taken the bullet” instead; the e has become silent (in many dialects), leaving the n.

• Despite those letters falling away, the process was not yet complete by the time the spelling began to be widespread and then standardized and reformed. That is, when the spelling veux was widely adopted, the letters more or less all had a value. But the process of erosion continued, leaving us with these redundant letters.

  • _{For “reformed”, note jlliagre’s comment about certain letters from Latin that were lost but were later restored by classicists. That means some silent letters are deliberate. Blame who you will!}

• Nevertheless, linguists are interested in exactly what status these letters have. For example, taking petit /pə.ti/ the feminine is petite /pə.tit/. The t ends up being pronounced. For those who can read this is easy to explain, but illiterate speakers also do this! How do they know which consonant to add to petit to form the feminine if they’ve never seen it written? Worse, it’s not always the same consonant: petit(e), chien(ne), vif(/ve), pompier(/ère), etc. So does every word have a separate rule for which consonant to add? Or do the words still have their final consonant in the mental dictionary, and a single uniform rule deletes it in the masculine?

• All languages undergo phonological change, and there are certain major trends, but they apply unevenly. Although French and the other Latinate languages are genetically related, they’ve been separate for so long that they’re as different as two species of the same family.

  • _{For example, taking the Latin word homō (inflected homin-) “man”, French happened to eliminate the unstressed syllable in the middle, leaving mn, and then assimilated those two nasals to mm in homme. The story in Spanish was similar but it ended up dissimilating them by turning the n into an r in hombre. This shows that we can explain why something happened, but it’s hard to predict what will happen next because there are multiple possibilities.}
  • _{Also note that the letter loss is not unique to French, as Eau qui dort wrote, but in other Latinate languages it’s mostly limited to certain dialects or the letters disappeared with the sounds and were never restored.}

That should give you the basic idea of what’s going on. The comments and other answers all give useful supplementary information.

In addition to Luke’s answer, here are some comments about each of your examples:

• Temps was often written tems, tens or even tans in Old French. When French spelling was standardized, the variant including p, despite being already silent, was selected because it reminds the p that was present in Latin. The ending s was pronounced at that time.

Unlike other Romance languages that have a phonetic orthography, and routinely changed word spelling to adapt to the pronunciation, French is much more conservative and often reluctant to accept such changes.

It is obvious when you observe the strong reactions to the 1990 reform that suggests using the logical ognon (which already failed to survive a previous reform) and nénufar instead of the etymologically bogus nénuphar.

Compare with Spanish which has no problem with nenúfar, elefante or fútbol.

• Roux was originally written ros or rous, then, as Circeus wrote, us became x to save parchment leading to rox. After a while, the x trick was forgotten and the u was restored to match the pronounced vowel.

Note also that there are some cases where consonants that were no more pronounced started to be heard again. This happened with infinitive ending -ir (e.g. partir which was pronounced parti). This is occurring now with the p in dompteur. In English, the t in often follows kind of a similar pattern.

Regional variations do also exist for a few words like persil or vingt where the last consonant is pronounced or not depending on the locutor.

One of the reasons the remaining words in your list have their ending consonant preserved is that it is pronounced when the liaison is made:

• pas assez (mandatory)

• deux ans (mandatory)

• beaucoup aimé (optional)

• chez eux (mandatory)

• petit homme (mandatory)

French would have been even more complex if we had different spellings depending on which word follows another.

McWhorter, J. PhD Linguistics (Stanford) outlines this on pp. 18-22 of The Power of Babel (2003). I post only pp. 18-19:

The Five Faces of Language Change

1. Sound Change: Defining Deviance Downward

Much of the difference between the Latin and the French sentences is due to the fact that in all languages, there is a strong tendency for sounds to erode and disappear over time, especially when the accent does not fall upon them. This is part of what transformed femina “woman” in the Latin sentence into femme in the French one, which is pronounced simply “FAHM.” The first syllable of femina was accented — “FEH-mee-nah”; the other two were not, and over time they weakened and dropped off completely. In real time, we process this kind of erosion as sloppy: to us, Jeet yet? is a barefoot version of Did you eat yet?, as inevitable but formally unsavory as an unmade bed. But this very process was part of what turned Latin into French, and not “sloppy” French but the toniest formal French.

Sounds do not vanish in a heartbeat; at first, there is just a tendency to pronounce the sound less distinctly in casual, running speech. What follows is a kind of analogue of “defining deviance downward,” a societal trend in which the gradual acceptance of behaviors once considered taboo has the effect of rendering behaviors of the next level of extremity easier to contemplate and fall into (“If smoking pot is no big deal, then why not…?”).

A generation that grows up hearing the sound produced less distinctly most of the time gradually comes to take this lesser rendition of the sound as the “default.” Meanwhile, however, they, too, follow the general and eternal tendency to pronounce unaccented sounds less distinctly and thus pronounce their “default” version of the sound, already less distinct than the last generation’s, even less distinctly. The next generation takes this muffled sound as “default”; but when they in turn follow the natural tendency to pronounce this sound even less distinctly much of the time, this time there is so little left of the sound that to muffle it is to eliminate it completely. Thus, for them, the choice is between making the sound at all and leaving it off completely. Finally comes a generation for whom the “default” is no sound in that position at all.

This erosion has a particularly dramatic effect in that, whereas some sounds in a word serve no particular purpose (the -ina of fem-ina), other sounds are part of suffixes or prefixes that perform important grammatical functions. For example, think of the -ed that marks past in English; without this suffix, one does not know from the word whether walked is present or past at all. The erosion of prefixes and suffixes like these was particularly central in turning the Latin sentence into the French one. There is a certain tendency for sound change to “go easy on” these prefixes and suffixes to preserve important aspects of the language’s machinery. But this is only a tendency, and just as often sound change wreaks its termite-like destruction even on the support beams of a grammar.

En trame de fond, indépendamment de la prononciation, en ce qui concerne les singularités orthographiques du français dont on traite ici et là (par exemple quand on dit dans une autre réponse que « [m]ost of these end consonants are no mystery »), il peut en effet être utile de rappeler que :

L’adoption du français comme langue royale [au 14e ; « au fur et à
mesure qu’ils ont été forcés d’abandonner le latin pour le français,
les officiers ministériels se sont donc rattrapés en se mettant à en
conserver les marques de latinisation de l’orthographe. »] se traduit
par une rationalisation et une unification de l’orthographe jusqu’ici
chaotique de l’ancien français (pour cœur par exemple on trouve les
graphies quors, cuer et quers). Alors que la graphie originelle
du français est davantage conforme à la phonétique (celle supposée de
l’époque puisque les preuves ne sont pas patentes) et parfois
arbitraire, elle est progressivement latinisée dans une tentative
d’aboutir à une « orthographe étymologique ». Ce qui n’est pas le cas
pour le mot cœur qui vient du latin cor, cordis (voir
Gaffiot). L’Académie française fige ensuite définitivement cette
nouvelle norme graphique qu’elle appelle « orthographe ancienne »
puisque procédant du latin classique, sans tenir compte du fait
que la Chanson de Roland, qui est le plus vieux texte
littéraire complet du français, a une orthographe totalement
différente – il épelle par exemple ki « qui » ou e « et » (cf.
italien e), etc. – ni du fait que le français est issu du latin
vulgaire et non pas du latin classique. Sont ajoutées alors des
lettres ne se prononçant pas devant les consonnes : là où l’ancien
français écrivait tens, le moyen français crée « temps », le p
rappelant son étymon latin tempus ; à partir de pois, le
moyen français crée « poids », le d rappelant la forme latine
pondus, ce qui constitue une erreur d’étymologie puisque le français « poids » procède du gallo-roman *PESU (< latin pensum, italien peso «
poids »), d’où « peser » et non pas de *PONDU, mais elle
distingue entre tous les homophones (ex : pois, poix) ; puis devient
en moyen français « puits », le t évoquant la forme latine puteus,
ce qui n’est pas tout à fait l’étymon, mais n’est, dans ce cas, pas
contraire à l’attraction qu’a exercé le vieux bas francique * putti,
phonétiquement proche, etc. L’immense majorité des singularités
orthographiques du français moderne est étymologiquement justifiée et
se rapproche partiellement du latin classique à l’origine du latin
vulgaire dont descend le français. […]

[ Contenu soumis à la licence CC-BY-SA 3.0. Source : Article
Réforme de l’orthographe française de Wikipédia en français ;
certains liens et mise en page légèrement modifiés, je souligne ]

La normativité et l’intervention de l’État, l’amour du et la fidélité au latin (classique) malgré sa connaissance imparfaite, la cohérence (homonymie etc.) et l’histoire sont des vecteurs de ces choix graphiques : « au début du XIXe siècle, l’orthographe se fixe et, contrairement aux autres pays romans, c’est le courant étymologiste qui prévaut et non pas phonétique » (Wikipédia). Que la consonne finale soit muette ou non, il y a eu dans la majorité des cas un désir de rendre, au moins en partie, morphologiquement (encore plus) compatible la graphie du mot avec ce qu’on pensait être l’étymon en latin classique…

So far and from a standpoint of scientific linguistics, Luke’s answer is the best one. For the sake of completeness and for those interested in the quirky side of things, here is a more formal rendering of the things involved:

1. Contrary to native speakers of English, native speakers of French acquire two grammars of their language in the course of becoming adults: Modern Oral French (MOF, coming with noticeable regional disparities) and Written Standard French (WSF, which is internationally taught in schools). These two “varieties” of French have different parameter settings for their grammars resulting in divergent typologies. WSF is the older one and its grammar functions mostly according to the rules of Old French. The historical change from Old French to Modern Oral French underlying the typological gap between WSF and MOF amounts to a shift in implementing grammatical features on lexical items from the right edge to the left, a shift a native speaker of French must familiarize himself with earlier (in school) or later and which most speakers never succeed in mastering fully.

2. WSF is largely suffical in implementing person, number, gender, case and intervening agreement features on lexical items such as verbs and nouns. In a sentence such as [Je [vend-s [le-s poule-s vivant-e-s]]], Je is the grammatical subject, the -s suffixed on vend agrees with the subject in person and number, the -e agreement suffix on vivant indicates that the poule complement is feminine, the -s suffixed on poule indicates its plurality, and the suffix -s on le and vivant-e indicates that they agree in number with poule.

3. MOF is predominantly prefixal in this respect. In [(Moi) [j-lé-van [lé-poul vivan+t]]], Moi is the grammatical subject which may be null, le j prefixed to lé-van agrees with the underlying subject in person and number, the +t is a so-called “floating” (or latent) consonant which indicates that the poule complement is feminine, the lé- prefixed on poule indicates its plurality, the lé- prefixed to the verb agrees with the *lé- prefixed to the direct object poul in number which is a very Bantu-like feature. Besides the edge reversal, what is also very new is that the masculine form of the adjective is derived from the feminine base by deleting the floating consonant which in reading the adjective aloud in a WSF text becomes “silent”. Suffixes on nouns have altogether disappeared and become a lot fewer on verbs: the 2nd person plural suffix -é, the conditional -rè or -ré (depending on the regional variety), the negative future -ra-pa, and the imperfect -è or -é, the later impeding the deletion of floating consonants in verbs such as in fini+s, imperfect fini+s-è, but fini-ra-pa. More prefixed modalities occur with the progressive antrind-fini-r or aprè-fini-r, the future I va-fini-r, and the future II pour-fini-r as in Moué chu-pour-la-fini-r la-djob, with the bonus of a univerbated chu totally opaque in most varieties if not all basilectal varieties.

4. Silent consonants in WSF texts are not “acquired”, as one competing answer would have it. As a general rule, before becoming “silent”, they were fully pronounced in Old French and silencing (or muting) amounts to a loss of phonetic realization over time. Learned restorations of Latin consonants in the course of standardization (such as the p in temps) are rather rare and unproblematic. However, silent consonants come in two different kinds, those that are silent for forever such as the plural -s and the p in temps; and those which in MOS float as +C to become silent only when occurring in context which are fully rule-governed.

5. Interestingly, working artificial intelligence models for spoken French are based on the MOF model of things. Models that need a subcomponent for silent consonants with ad hoc rules for silencing are problematic. As it is, only second language learners have the “chance” to acquire both grammars of French in an order that is not chronologically inverse, going from WSF to MOF.