Yup frankish tribes got settled in roman territory and interbred very early on with romano-gaullish elite families (landowners, governors, military heads, etc). They were a client-tribe of Rome and used as a shield against other intruding germanic tribes. Which is why they addopted christianity (non-arian) so early on compared to other germanic tribes.
You also have to take into account that modern day France was at the time home to various distinct languages/ethnicities, breton/norman/langue d'oil/langue d'oc/arpitan/catalan/basque/etc (even those classifications put several groups together, particularly langues d'oil and langues d'oc which had numerous distinct "flavours" in themselves)...langue d'oil is the one that eventually became known as "french", and some of it's earlier incarnations had traces of germanic language influence, but it was still almost entirely derived from "vulgar latin". Not unlike norman and scandinavian influence in the language, which was negligeable.
edit: Found a ethno/linguistic map of what was considered Gaul in the 8th century (with the addition of Corsica for some reason, probably cause it's considered part of modern day France. Which doesn't explain why they'd add Walloons and Flemish and early Swiss in that case, but whatever):
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loginSecond edit: Afaik the Franks were not one unique tribe with one particular language but a confederation of many different tribes, and it's possible that they addopted the vulgar latin of their subjects as a common lingua franca (haha).