It was the other way around: at some point people realized that French was not Latin (i.e., it was no more vulgar Latin=colloquial language, but a language in its own right.) Similar thing happened to other descendants of Latin - like Spanish or Portuguese.
Wikipedia on the History of French:
Frankish had a determining influence on the birth of Old French, which partly explains that Old French is the earliest-attested Romance language, such as in the Oaths of Strasbourg and Sequence of Saint Eulalia. The new speech diverged so markedly from the Latin that it was no longer mutually intelligible. The Old Low Frankish influence is also primarily responsible for the differences between the langue d'oïl and langue d'oc (Occitan) since different parts of Northern France remained bilingual in Latin and Germanic for several centuries, which correspond exactly to the places in which the first documents in Old French were written.
(emphasis is mine)
Note that the name of the language itself, français is a reference to Franks (aka language of the Franks), of which the most famous is Charlemagne (Karl the Great), who has personally done quite a lot to encourage literacy. In particular, the description of one of his minor military campaigns, The Song of Roland (La Chanson de Roland), is regarded as the first major work in the French language.
Rusticam romanam linguam
A Council of Tours in 813 decided that priests should preach sermons in rusticam romanam linguam (rustic romance language) or Theodiscam (German), a mention of Vulgar Latin understood by the people, as distinct from the classical Latin that the common people could no longer understand. This was the first official recognition of an early French language distinct from Latin.
In other words, up to this point Old French and Latin had been treated as the same language.
The Oaths of Strasbourg, considered as the first extant text in French, was written in 842, i.e., after the council of Tours of 813. The text was apparently explicitly written in the local Romance dialect, rather than in proper Latin.