That would make sense, considering that the Franks were a Germanic tribe, and ended up speaking a Latin derivative. But of course, they would not have needed to import the Latin from Rome, since Gaul had been a Roman province for hundreds of years, and Latin would have been the "lingua franca" even after the collapse of Rome. So the Franks picked it up from the natives.
Gaul was a province, but when the Franks came in they didn't just except the "common speech" of their new peasants, any more then they at first excepted the Religion of the Romano-Gauls. Clovis, after excepting the Catholic faith, would have begun enforcing the new language among the upper class Franks, but after he died the Kingdom feel into a bad-spell. Later, Carlos Magnus commissioned schools(monasteries) for the purpose of revitalizing western Civilization, and they would have included Latin as an obligatory language of government as well as Religion. Latin became the universal written language of Europe; you could send a message anywhere to anyone, as long as it was in Latin.