It depends on the place. In France for example it was always considered the language was gallo-roman, because they never completely spoke Latin. Latin was the written language, but the spoken language was a mix of celtic and Latin. And by the XIIth century it was old French. Southern France, occitan is even worse: it started to be latinised in the IInd century, and mixed again with celtic in the VIth century.

Those languages are roman languages, so they indeed are majorly Latin in their origin, but they never were actual Latin. It's not even sure most people actually ever spoke Latin. It was very common in the past to use translators to communicate.