Laïcité - Wikipedia, the free encyclopedia).
France is one the most (if not the most) secular state in the world, and also holds the highest % of strong Atheists in the world (between 30 to 40%, according to polls. See-> Fichier:Europe-atheism-2005.svg - Wikipédia).
It took a long a long time for the French goverment to tame the Catholic church (1905 French law on the Separation of the Churches and the State - Wikipedia, the free encyclopedia), and hence it cannot tolerate from others what it already doesn't from Catholics.
Hence, in public administrations or state schools, no conspicuous religious signs are allowed. It means that one can wear something very discreet (like a small crucific, a star of David or an hamsa), but NOT a kippa, or an headcarf.
The French Jewish community has always "played the game", and respected the French law to the letter, so they never posed a real problem. As a matter of fact, the 1905 law allowed them to become more emancipated than ever. With the Catholics, as aforementioned, it took decades of long lasting feuds, but eventually they were subdued.
With the Muslims, well, at first, this community never created a problem. Radical Islamism, as we know it, arose only during the 90'es, so it's a very recent issue. And let's not be hypocritical, for those militants, it's not a question of religious belief (according to polls, a majority of French muslims agrees with the 1905 law), but it's rather a POLITICAL issue.
Wearing the hidjab or the burqa is not a question of faith: it's rather a way for young Islamists to express a political message. And hence their tactics is to deliberately seek conflict with the law: it gives them a tremendous publicity in the medias.
It's also a way to express their disagrement with the current French and Western values: they say they don't wan't to be a part of the French society, and never will be. And when they say they don't want to live with us, they totally reject the process of sociological integration and desegregation, which lies at the cornerstone of the French Republic: equal rights and duties to all, no exception, no preferential treatment!