It's based on social codes more than anything, similar to other countries. There are preferred vectors of transmission for such codes. In France some schools my play a part but I don't believe it's so segregated. The role of grandes écoles is overblown and they're not nearly as influential as Ivy League schools and Oxbridge are in the US and UK. I'd say the high school you went to is probably a more important factor, as are the extra-curricular activities you were doing growing up, in deciding which class you fit in.