In Season 1, Episode 4 of TNG, Data calls French an “obscure language”. Combine that with “French” people like Picard not speaking it, and the show seems to at least heavily imply that it died out at some point in the past (maybe outside of academia at least).
In this previous thread, the discussion of languages in Star Trek, and the idea that every species had just one language (including humans of Earth) started here: