Oh, come on. Using a language to stand in for an ethnolinguistic group to stand in for a culture is such common practice that - it actually doesn't make sense to me to criticise it, what are you criticising? Just because someone speaks Hungarian doesn't make them a Magyar, but it's pretty clear that Hungary is Hungarian because the Magyars, speaking Hungarian, a Uralic language invaded it.
On the other hand, linguistical differences might not have played a major role into ethnic or tribal differentiation : we know several instances of Germanic peoples having either Celtic (Gaulish) names or some of their kings having Gaulish names as well. It really was something that appeared with Greeks at contact with peoples of the "far corners" and even there it mostly got down to "everyone sounds like retards but us" rather than "everyone have their own specific language". At the very least, the disdain for written forms could point a lesser sacralization of language in some peoples and a lesser importance given to linguistic "identity" among Iron Age Europeans.
To use your example, France is French not because the Franks speaking Frankish invaded it, but because Franks were significantly romanized and mixed up political identity and language identity. Eventually, I'm not French because I'm speaking French, but I speak French because I'm French does highlight the complexity of the relation?
It's quite possible that without the essentialisation of language as identity (which is really something that was not systematic before the Middle-Ages/Renaissance) simply didn't played a major part into differentiating Celtic peoples from,say, Germanic or Iberic peoples. We suspect material culture didn't either.
In fact, a good part of the distinction between Gauls and Germani wasn't linguistic (both people seems to have been speaking something close), ancestry (as they acknowledged being relative, Germanics or Celtics) but well based on geopolitical considerations, at least until Greeks and Romans kicked it and essentialised differences they understood or considered themselves (as it happened with colonized people in the XIXth century)
The hundreds of lexical correspondences between Goidelic and Brythonic? Did they maybe make up Proto-Celtic as a whole?
To be fair, the obviousness of connection between Goiderlic and Brittonic Celtic speeches is partly the result of romantic historiography : there's a whole debate about this, but I tend to think it decredibilized the Gallo-Brittonic hypothesis on non-scientific arguments.
And, technically, people did made up Proto-Celtic up to a point : it's not an actual language reconstitution as we can do with Gaul or Britton, but a series of attempts extracting roots and feature proper to Celtic languages. Now, this is not a problem at all as long we remember the nature of Proto-Celtic elaboration IMO.