What are you talking about? Basic education in France is free, the university is open to everybody and is not expensive at all; and if you are a good student you can even go to a "grande école", which is not only free but you receive a good monthly salary just to study there. The entrance exams are open to everybody, and they are anonymous. Please tell me how can it be any less elitist than that!
Of course, there is a lot of social inertia whereby children of parents with higher education are more likely to pursue a higher education. But this is an acknowledged problem and one of the main goals of the system is precisely to solve it.
Source: I am part of the French higher education system to which I entered as a total outsider.
(you are right, however, that the private employment system is awfully elitist: if you didn't go to the right schools it's much harder to get a good job)
It does happen…
Owning a house? Check
Starting a business? Check
Starting a family? Check
Getting an advanced education? Check
The US is full of opportunity and "chances". Just because you feel nobody has a chance does not make it so. Nothing is for free - you need to be willing to put the effort into making it happen.
The company I used to work for had the HQ in France, and there, all the devs doing the stressful mediocre pay grunt work, were all Mohamed and Ahmed immigrants from North Africa, while all the suit & tie managers with expensive haircuts doing nothing but have coffee and joke around for 4 hours/day, were native white French dudes.
I wish this was a meme though, but this is my anecdote from my time there.
Who cares? France gives everybody mobility, a computer and network, plus free training in case they cannot go self-taught. Most of French new jobs are deliviery and remote work by African immigrants (extensively represented due to France having half Africa as a former trading point, faith territory and colony).