Historically, in Old French, ne conveyed the negation, with the n- prefix that conveys negation in many Indo-European languages. The second negative particle was an adverb that clarified what was negated: “ne … jamais” = “not … ever” (i.e. “never”), “ne … aucun” = “not … one [of a set]” (i.e. “none”), etc.

Over time, it became the norm in French to systematically include a second particle, even to negate a yes/no statement. This probably happened because the ne negation was unaccented and so easy to miss. Where there was no adverb to negate, a suitable noun was used instead.

Je ne vois personne.   (lit. I don’t see any person.)
Je ne vois rien.   (lit. I don’t see any object.)
Je ne vois point.   (lit. I can’t see any point.)
Je ne mange mie.   (lit. I don’t eat any crumb.)
Je ne bois goutte.   (lit. I don’t drink any drop.)
Je ne dis mot.   (lit. I don’t say any word.)

Over time, those nouns were standardized down to a few: personne for people, rien for things, point for simple yes/no statements. Since these words no longer have their original meaning, don’t vary, and can be used even with verbs that don’t take a direct complement, they have become adverbs. You can find traces of the nouns in a few set expressions such as “Qui ne dit mot consent” (lit. “he who says no word agrees”).

Ne … point used to be the standard negation, but nowadays it’s very old-fashioned. I think it mostly disappeared from literary usage in the early 20th century and from regional usage in the mid-20th century. Ne … point cannot be considered standard in modern spoken or written French. The standard default negation in modern French, is ne … pas.

While the use of ne without a second particle hasn’t completely disappeared, it is not standard modern French, and is very rare even in literature. It can be found occasionally in poetry.

In most sentences, either ne or the second particle (pas, rien, jamais, …) is enough to convey that the sentence is negative. Words like rien and personne would require an article if they were noun, and adverbs like jamais and articles like aucun were rarely used without a negation. In modern spoken, informal the second particle is often considered enough, and ne is omitted. Thus:

Je vois personne. Je mange rien. Je dis rien.

This is informal language only, mostly spoken. Ne can also be omitted in some informal written contexts such as emails or chat messages between friends, but it wouldn’t be omitted in, say, a newspaper article, or a formal speech.

In summary, a negative marker like jamais, rien, aucun, etc. is a negative marker when paired with ne in standard and literary French, and alone in modern informal French. It is not necessarily a negative marker in old-fashioned literary or poetic French. When you see such a word without ne, you need to evaluate the age and formality of the text to determine whether it is negative or not.