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.