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.