Yes, but while in political terms the Gauls, Romans and Franks were distinct entities, in cultural terms the region was more of a melting pot. The Roman conquest of Gaul ended up blending their two cultures into a new, distinctive "Gallo-Roman" culture (see https://en.wikipedia.org/wiki/Gallo-Roman_culture), for instance, and then when the Franks came along their culture got blended in as well. So modern French identity has strains in it running back to all three sources.

The Frankish kings were a small minority of rulers and did not actually leave much Germanic influence.

The modern French culture is a direct descendant of Gallo-Roman culture, which is basically Roman culture with a little Gaulish influence.

Of course, but a nation identity is built on more than just facts.

> Of course, but a nation identity is built on more than just facts.

In fact, a state's national identity is based on almost anything but facts.