Je parle français, subject–verb–object, is the simple affirmation.

Negation is formed with the particle ne (often omitted in speech) and usually one (or more) additional words to mark or nuance the negation. The adverb pas expresses plain negation and is the most common mark of negation.

Ne always precedes the verbal phrase, and pas usually follows the inflected part (be it the main verb or an auxiliary).

Il ne parle pas français.

Je n‘ai pas lu le journal aujourd’hui.

Negation using other “negation adverbs”:

Il ne sort jamais.

Je n‘y crois guère.

Il ne dort plus.

(Semi-?)negation using indefinite pronouns:

Il n‘a rien mangé.

Il ne va nulle part.

Personne ne veut venir.

Aucun ne convient.

Or with a combinaison:

Il n‘a jamais fait aucun effort.

Personne ne dit rien.

Aucun n‘a jamais convenu à personne.

Rien ne va plus.

Note that pas does not combine with other negations. Though, pas may negate a normal adverb.

Il n‘a pas encore vendu sa voiture.

Etc.

One last remark related to your “*je ne pas” experiments: ne and pas actually come together when negating an infinitive clause:

Je le note pour ne pas oublier.

But an infinitive clause never includes a subject; “*je ne pas” isn’t a valid word combination.

A literal gloss of the individual ‘words’ would be something like this:

Je ne parle pas français.

I [negative marker] speak not French.

To an English speaker, it can look like the order of the words is "the wrong way round". But it turns out that in French, the order that you see reflects how French works generally.

A key thing to understand is that in French, the ‘word’ "ne" is actually not a ‘normal’ word, but rather it is what is technically termed a clitic– if you like, a half-word-half-affix (or in other words, its status is similar to the -n’t in English (cf "didn’t")). The pronoun "je" also has a similar status.

So in effect, "je-ne-parle" is a single word on a syntactic level. To a French speaker, there’s simply no possibility of putting another word such as "pas" (which is really the actual ‘word’ that is signalling "not") in between the subject and the verb, just as to an English speaker there’s no possibility of putting anything between "did" and "n’t" in "didn’t"[*].

Partly because of this and partly because of how French verbs work generally (for the technically minded, due to a phenomenon termed "raising"), this means that there isn’t a natural "slot" in French between the subject and the verb in which to place an adverb in general. So whereas in English one would say "John often goes…", in French, the word order would be "Jean goes often…"– there’s effectively no "slot" to put an adverb in between the subject and verb in French. (Technically, the difference is often analysed as the verb "raising" to different syntactic positions in English vs French, but that’s not too important here.)

So, what you essentially have in French is a combination of (a) the special ‘negative prefix’ (clitic) "ne" that French attaches to the beginning of verbs to signal a negative, and (b) the negative adverb "pas" appearing in what is the natural place for an adverb in French.

[*] They’re actually not quite analogous. But broadly, the point holds.

“Je ne pas …?” has no meaning, and can’t be the beginning of a sentence in French.

Ask Google to have an idea of how Google Translate works. There is no syntax rules in the program, just a gigantic collection of billions of sentences, and it is fast enough to proceed by comparison and assimilation.

It works pretty well for ordinary sentences ; it can’t be really good for an unusual use of the language, such as poetry. And for funny results, try an absurd sentence, however grammatically correct, such as “The angry star has deep roots in the marshy seas sleeping on top of the cellar”, and then backwards …