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.
Which was my original point: I do not care what someone's ethnic background or country of origin is, as long as they are willing to fight and die to preserve and uphold the US Constitution.
That's a patriot.