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.
This is assuming that the "natives" spoke Latin and not some corrupted mishmash of developing what we now call French. If the natives spoke some "pidgin" tongue, then actual Latin would need to be brought in from Rome.
I don't know what the actual case is, but it was several hundred years from the end of the Empire, so it wouldn't suprise me.
SD