Of course not everyone is graduating with a technical degree, but coming from Germany where top politicians often don't even have a finished university degree and high-ranked politicians are regularly found out to have been plagiarizing their PhD work it was pretty impressive to see a working elite system. It also has some negative aspects and nepotism is a thing as well (in the sense that people who went through the system know how to game it to get their children in with high probability) but it's much better than what we have here, in my opinion.
Germany was and still is scared of anything that can be considered elitist as people always associate it with the elitism from the Third Reich.
1/ énarques aren't technical at all, don't actually know anything except how bureaucracy works, and yet they're in charge of everything
2/ super-selective schools have the side effect of letting people think they're geniuses because they topped a competition while in their teens
That's a misconception. ENS has two branches, science and literature. ENS Sciences is technical, the other isn't. X (Polytechnique) is an engineering school in theory, but in practice very few of its students become actual engineers.
ENA is essentially a law school; it's even less than that, it only teaches how the French administration works, not law.
The one thing these schools have in common is that they are extremely competitive, and select for extreme dedication (and a bizarre capacity to study with high intensity at an age when other people are dating or partying).
But at the top level of the French government you mostly find only énarques (= people who attended ENA); they are not technical in the least, "don't have a clue about technology", but think they know everything. It's a terrible, terrible system.
Source: am French.