The number of women bathing in burkinis in France is extremely small, probably similar to the number of women who want to walk around the Riviera these days in a full burka: hundreds rather than millions. Women in Muslim countries all around the Mediterranean have somehow managed to work around the issue for decades without burkinis and nobody cared, but now people on both sides want to make it An Issue. As often, politicians are trying to gain a little advantage, one year ahead of important elections, by solving problems that either don't exist or are incredibly minor, just so they can be seen to be doing something. It is easier than doing something about the many big problems that France faces. Most of the very few mayors that have passed an ordinance on the subject are apparently in areas that have never seen a burkini. They were probably the same mayors who were banning monokinis 40 years ago. The fact is they have the power to do that.
Some background on the French concept of laïcité, which is important. The secularists fought the catholics for a good century and a half all over France, and they won in the early 20th century. There is a total separation of Church and State, religion must be a strictly private matter, you won't catch Hollande saying "God bless France" at the end of his speeches, etc. If you want to wear a cross on a pendant in school, you have to stick it inside your T-shirt. The French are not going to make exceptions for a few radical Islamists who have suddenly decided they want to make a point about what should be the proper dress code for women à la plage.
I have no idea what the right approach should be. I feel people should be able to wear whatever they like, and Muslim women should be able to go to the beach just like everybody else. On the other hand nudists know they should go to a nudist beach if they don't want trouble. If I wander onto a nudist beach I have to either leave or take my clothes off, it's the deal. Maybe there should be a few burkini beaches.