Usually, before accessing those schools, you have to study for 2 years in a preparatory program called a Classe Préparatoire. Point is, the best can be quite expensive.
The most egregious thing though is that during school holidays in France, some private organisms (in Paris) offer 1 or 2-week cramming programs for €10-15k a pop where you get tutored by the very people that write the entrance exams to the most prestigious schools.
Wealth is a key.
Wealth definitely helps in the sense it gives you a better environment to support you during your studies. About it helping you being tutored by fancy private organisms, this is true but I think it applies more to the "lower" part of the Grandes Écoles & co pyramid. You are not going to enter Polytechnique or ENS solely because of that. It still requires a lot of work or talent.
About the set of high schools/classes préparatoires funneling a large part of candidates to top schools, that is definitely true. But again it requires a lot of work, you are not going to move through Henri IV or whatever to ENS only because your parents have money. But receiving a good education from birth and having family and friends who knows how the system work, because they moved through it themselves, helps a lot.
But wealth helps because these places are usually in large cities (and mostly in Paris), which are expensive to live in. And to get there you have to come from good/prestigious high schools and have good grades, which again living in a wealthy family helps a lot.
Entry into Grandes Ecoles is usually a function of three things: knowledge, preparedness, and, indeed, talent. But that last variable has a much lesser effect that what people tend to assume.
What's interesting is what they put the emphasis on. Polytechnique is probably the most theoretical math heavy engineering program I've ever seen.
It's probably better exemplified by an anecdote from someone who did a double diploma from Polytechnique Paris and Montreal. He got flak in Paris for solving a problem using a numerical approximation, because there was a way to get to an exact answer. And in Montreal he was asked by a professor if he could "borrow his micrometer CNC machine" since he gave an answer that was way too precise for the material whatever he was working on was going to be made of.