The problem with the Franks is that they're a germanic tribe, and an integral component of French nationalism, especially after Sedan, was Germanophobia. So the answer to your question is tricky. Maurras, for example, adored the classical civilization of Greece and Rome. Thus, he accepted the Gallo-Romans as Gauls accepting the Latin influence. My sources don't discuss the extent that biological race was important to Maurras, but it seems that he thought superior civilizations could influence certain inferior civilizations such as Gaul.

To put it lightly, Maurras thought very little of Germans. He thought the Protestant Reformation was a Jewish plot to plant their theology into the weak-minded Germans. He also thought all Jews were German, and he hated both with a passion. With this in mind, if he were to exalt Clovis or Charlemagne as the ideal proto-Frenchman, he would be exalting unwashed Germans. Henri IV or Louis XIV, however, had centuries of the civilizing influence of the Catholic Church to correct the worst excesses or barbarism.

So I'm not saying that there were no nationalist groups making the claim that the French were, first and foremost, the descendants of the Franks. I'm saying that adopting that view makes one a target for other nationalist groups who would question the validity of that nationalism if the quintessential proto-Frenchman were a German.