I won't argue with the essence of your point though, although, for what I know, much of the nobility up to the 1800's was of Frankish descent, while Gallo-roman blood dominated among the commoners. So some heritage was there indeed.
I think the goal of using 'our ancestors the Gauls' was to create a shared history, to promote a national identity, without any regard to the actual ancestry of the actual population.
Also you have to put back the origin of this idea in his context: it's coming from the XIXth century, when moving away from the monarchy. The Gauls served as a common ancestry, without any reference to the previous monarchies, which explain why it was pushed by Napoleon III (who started up excavation looking for the site of Alesia) and the IIIrd Republic.
The part I had in mind is the old “our ancestors, the gaulois” which is not taught as is anymore, but still stays very present in the minds through an almost exclusive focus on Gaulois’ side when depicting that time period (not just fantasy depictions like Asterix, but also a lot of documentaries and reconstitutions funded publicly)
PS: for additional context, vikings were around the 9th century. I am not pointing at just current trends.
Some Vikings were exiled from what was Wessex, East Anglia etc., but became England.
This is why posh people in England sometimes call their dog "Rollo", Rollo was the Viking leader that the Normans descended from. The people that went on to invade England.
None of this invalidates the idea of France or England or French or English.
Ps. You were pointing to current trends, hence pointing toward Paris and peripheries or "four or five generations ago"
Going to Normandy nowadays and looking at general public exposition it’s make pretty clear their ancestry is mostly from the Vikings and Nords.
In the east it’s also clear that their frenchness is a fluctuating and partial attribute.
All around the country, each region have a very clear multi-cultural past. And Paris and its periphery is a huge Petri dish of people coming from around the world with a significant number of families that have no ancestors that were in France more than four or five generation ago.
Books still present Franks as french people’s ancestors, but I wonder how teacher make it match with the reality when they teach their students.