Wearing the full veil has become a hot-button issue in France, but the reasons may not be immediately obvious to many of those who don't live there. If countries can be said to have ideas of themselves, then assimilationism, the notion that Frenchness is a matter primarily of culture rather than birth, is an element of France's idea of itself. And "culture" here implies acceptance of certain substantive principles. Note, in the BBC article linked above, the French immigration minister's reference to "the principles of secularism and equality between men and women," acceptance of which is considered, at least in this official view, part of what it means to be French.
I recently had a conversation with the sociologist Rogers Brubaker (ah, the pleasures of name-dropping), and afterward I took a quick re-look at his book Citizenship and Nationhood in France and Germany (1992), which I had read a long time ago. The book brings out, among other things, what Brubaker calls "the weakness of the ethnic moment and the correlative strength of the assimilationist moment in French self-understanding" and the way in which Frenchness has been defined "in social and political rather than ethnic terms, as a matter of social becoming rather than intrinsic being" (p.112). For his bio and more recent books, click here.
P.s. Two relevant blog posts: here (from last July) and here.