The Franks were French, after the 7th c. or so. By the time of Fredegarius, their Germanic origins were all but forgotten. For nearly the entirety of the Middle Ages, « Frank » meant a Catholic of Gaul who's cultural language is Latin or a Catholic, depending on the context.
That's a dichotomy that's fairly recent in historiography, and doesn't at all fit with historical usage. If memory serves right and came about in the wake of the rise of the Bourgeoisie and the French Revolution, with the need to conveniently give the nobility a foreign tint.
Moreover the Germanicity of the so-called barbarian tribes, including Pre-Merovingian Franks, has to be reassessed now with what we know about identity politics in the Late Roman and Post-Roman World. People might have played at being barbarians a lot more than actually being it, in a very comparable way you see Americans pretending to be this or that.
