This assumes that "X belongs to Y" means "X is a possession of Y", but that simply isn't the only meaning "belongs" has: it also means "is a part of", for instance. You can belong to a club without thinking that it owns you. FWIW, the oldest meaning of the word is more like "accompany" or "go appropriately with".
I don't know whether appartenir has a similar range of meanings, but my guess is that it does.
It does - indeed in French the second meaning, "is a part of" is used much more frequently than its English equivalent, and is clearly the sense of the word that Sarko was using.
I don't know whether appartenir has a similar range of meanings, but my guess is that it does.