The Franks were a group of Germanic tribe located near the Rhine river. They were one of the many groups that went up against the Western Roman Empire during its collapse. The Frankish tribes expanded into Roman Gaul and established their kingdoms. The king of one Frankish tribe, Clovis, eventually became more powerful than the other Franks. He conquered and united the Frankish kingdoms and gained control of much of modern day France. The Franks became a massive presence in Western Europe and held their kingdom for hundreds of years.

Names such as 'Gauls' or 'Franks' (or even celts) are often given by outsiders (Romans/modern day historians) and are often misheard corruptions of genuine terms from the insider group. If the whole ethnic identity historic debate has taught us anything it is to not place too much emphasis or importance on such labels.

So the people who the Romans labeled as Gauls, as Franks (and as Celts) may or may not have referred or understood themselves in such terms. These terms have been kicking around for a long time (Celt since Herodotus/Gaul maybe Herodotus as well but I can't check at the moment/Frank since the Augustan History - which is hard to date).

So in short we don't know. But more precisely we don't need to know as precise labels aren't that helpful.

For example 'the beaker people.' They certainly didn't call themselves that and it's only purpose is to give them a name for so that it is easier to discus them today. Gauls and Franks should be thought of in the same way - convenient labels, not strict definitions.

Better late than never.

The Franks took over Gaul (the area), but they were a very limited tribe, as far as number are concerned. Culturally speaking, by the time of Clovis, Gaul was much more Roman than Celtic (Gauls). The brilliant move of Clovis was to actually convert (and have his warriors convert) to Catholicism, which was the main religion of the people and rest a big part of his power on the bishops. From then on, he was no longer an invader. Unlike many other German invaders that just passed through (like the Wisigoth, the Vandals, etc.), the Franks, assimilated "quickly" with the locals since they eventually took on their customs.

A Germanic tribe called the Franks migrated and took most of Gaul, which is modern day France. So the Franks became the French. Gauls or celts only have a magority in modern day Brittant in France, kind of sad knowing how fiercly the Gauls fought for Gaul especilly against the Romans. Only to loose it to the Franks, and today are pretty much gone except for what little Gallic/celtic remains in Brittany :(