I believe they do not write their names on exams so that the grader favors not the ethny.
Actually, both names and student ID numbers are required on university exams. This is actually contentious as it results in clear biases. French professors can be extremely biased and won’t hide it.
Or do you mean the entrance exams? That’s about the only unbiased part of the system and even then there are ways around it.
In any case, France is an interesting case in terms of discrimination. Officially, it doesn’t exist and anyone can become anybody. But in reality there’s a small elite that perpetuates themselves. It’s incredibly difficult for a french person to go to a grande ecole if their parents did not go to a grande ecole. A lot of this has to do with how the system works: If you didn’t know you wouldn’t know which high school to send your child do, which prepa to enroll them in, etc. Because they can say that those who graduate from the grande ecoles (and the tres grande ecoles) did so only by merit they can ignore all these factors and the result is the white French elite continues without outsiders. An interesting aside is that there are, in fact, some outsiders but they tend to be children of Asian immigrants. Arabs/North Africans are a tiny minority and blacks are non-existent except for a few foreign African students whose parents tend to be very well connected politicians or business people in their respective African country.
Just out of curiosity are you (formerly) French or do you just like the south of France? I vacation in Villefranche-sur-mer most summers, not very far from the Var. It’s a beautiful area.