Yet he grew up in Algeria, the son of a Spanish mother and an Alsatian father (who was born in France, but grew up in a German-speaking home) and did not set foot in Europe until he was an adult.
Also the father of French New Wave cinema, Jean-Luc Godard, grew up in a Swiss Protestant household and was of Swiss-French, Swiss-German, and Danish background.
They both adopted - and helped create - mainstream French culture - and they are considered purely French.
The average Frenchman does not view them as interlopers, or somehow "off."
The most important characteristic: do they consider THEMSELVES French, give France their primary loyalty, and give confidence to the Frenchmen around them that they are loyal to same idea of "France"?
For me, to consider somebody an "American", I would need to have confidence that they are loyal to America and their fellow Americans, and that this loyalty is senior to any loyalty to any non-Americans.