I don't want to get into morality, but this would be unconstitutional. In fact, the rights of minority's are arguably the main reason there is such a thing as a Constitution at all. It is in western society deemed to be a vital condition for popular sovereignty, and hence for the rightfulness of democratic process.
To what extent do they agree on this is doubtful, AFAIK U.S Constitution is one of a few that has some meaningful safeguard built in for the rights of minorities. In France for example, as long as it's approved by the parliament the minority is pretty much screwed. Examples including he hijab prohibition, and the criminalization of Armenian massacre denial speech.
Have those cases held up in court? 'Cause that's what really matters, of course, in regard to the constitution.
The western tradition I speak of is basically the Enlightenment tradition, derived from the likes of Locke, Hobbes, Rousseau and Kant. Ideals that instigated the American and - especially - the French Revolution. I'm not French and I do not know what the current French constitution says exactly, but I'm like 99,99% certain minority rights are protected, since such ideals were a major motive for the revolution: http://en.wikipedia.org/wiki/Declaration_of_the_Rights_of_Man_and_of_the_Citizen
Also, I don't think you can be part of the EU if such protections for minority's are not in place. This one I'm less than 99,99% sure on. (UK doesn't have a Constitution at all, so...)
As for the hijab, if this has stood up in court, my guess is that they claimed that hijabs suppress women, or something like that. Hence, they actually banned them to protect women (= 'minority') rights. You may agree or (like me) disagree, but if this issue (or the Armenian thing) did indeed hold up in court, it probably says more about the individual judge than anything else.
I don't know much either, but I think the focus of the problem is how you prioritize people's rights(French seem to favor equality over freedom of speech, unlike the U.S Constitution), and if effective measures are built into the Constitution to make sure it's respected, U.S Constitution's 2/3 state legislature approval requirement for amendment is a pretty strong protection clause IMO.
The French Constitutional Council do work to check if parliament statutes are in conformation with the Constitution, but the justice selection process, I think, leaves a bit to be desired, from Wikipedia:
Following from the 2008 constitutional revision, appointments to the Council will be subject to a Parliamentary approval process (Constitution, articles 13 and 56). As of August 2009, these provisions are not operational yet since the relevant procedures have not yet been set in law.