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Racism - headscarves were also a symbol of anti-colonialism. French soldiers, when invading Algeria the previous century, saw the headscarves and hijabs as a "foreign" wall, keeping them from their "prize". In the modern day, headscarves and kippahs are seen as threats to France's "perfect" "assimilated" society. France wants to celebrate their national identity and culture by removing any differences in their culture.

As such, the ban is mostly only enforced on Muslim and Jewish symbols.

Sexism - much of the justification for the religious symbol ban is that it protects children who are "pressured" by their cultures to dress a certain way. Yet, by that same measure, the headscarf ban is about the French government controlling women's bodies.

Religious-ism? - what's most interesting about France is how differently they approach the separation of church and state. In America, this separation is to protect religion from the state. In France, its to protect the state from religion.