Normandy is a small region in the north east of France. Brittany is a small region in the north west of France.
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"
PS: for additional context, vikings were around the 9th century. I am not pointing at just current trends.