France, thankfully has a culture where sex and nudity aren't seen as "dirty" or "immodest". In short, the question is not about religion, it is not even about a costume, it is about a symbol. Marianne has been a national symbol of the French Republic since the fall of the monarchy in 1848. She is an icon of freedom, democracy and opposition to monarchy.
I wonder if the women wearing the headscarf would object to anyone wearing a bikini in Muslim countries. They'd be up in arms about these bikini-clad women corrupting their men and destroying their culture. If other countries can hold on to their customs, even if they are abusive, then France has every right to say that the breast and not the headscarf represents France.
Yes, France has it's priorities correct. Naked breasts probably do represent France better than a headscarf as the French are noted for their nudity. However, this does not mean I agree with it. There are many who are offended by nudity, so France should not advertise their naked breasts as representing France.
Yes, naked breasts go with the oh la la image of sexy French people and topless beaches, but forcibly making a women take off a burquini is a personal and religious violation. I don't think that's something that most people would want to represent France either. I get that there's concern and fear over terrorism, but if a woman chooses to express her religious beliefs by wearing modest dress, that's normally not hurting anyone.