The fine is doubled for forcing a minor to cover up. You can see from the structure of the punishment that the government's intent is to protect women from subordination by private citizens. The premise — is it proved? — is that a woman is highly unlikely to freely choose this form of religious garb for herself. The freedom of women who choose the veil is counted at nothing compared to the supposed great evil in coercing women to wear it. If the coercion involved is so terrible, why not only outlaw coercion?
But is intrafamily coercion really that bad when what we're talking about is clothing? Would you be willing to accept a generally applicable law that imposed a 1-year jail sentence for forcing someone to wear clothing they don't like? Don't parents and spouses do that all the time? Would you double the sentence — on a generally applicable law — for parents who force their daughters to wear something other than what they want to wear?
Once you start asking questions like this, it is hard to avoid the conclusion that the French law is anti-Muslim.