Not true.

What happens, and not only in France (it's like that in the UK as well), is that primary and secondary schools that are in not very good areas are not ambitious for their pupils. They'll say average is fine, going to a technical college is very good, etc. so in the end those pupils do not think of taking the "high road" because they've been convinced it is not for them.

On the other hand, if your parents are highly educated and you go to one of the top secondary schools you'll be pushed and told that you should work hard and that you can get into a top university.