If seeing a woman in a burkini makes you uncomfortable, that is YOUR problem, not hers. Bad_azz's comments about segregation were completely relevant. A major reason behind segregation in the US was because it made white people uncomfortable to have to share drinking fountains, bathrooms, or bus seats with black people.
As to "reciprocity" (ie, if Saudi Arabia or other Muslim countries don't allow bikinis, this grants France the right to deny burkinis), it is illogical no matter how you dress it up in pretty language. For one thing, it confuses acts of the state with decisions of the individual. The two are not the same. Take me, for example: if America continues to lose its collective mind and actually elects Trump as president, I trust none of my fellow posters will confuse that official act with what *I* believe and what actions *I* choose to take. Likewise, a burkini-wearing woman in France cannot be held responsible for the laws of SA. You have no idea whether she agrees with those laws or not. It's entirely possible she believes women are enlightened enough to make their own choices, religious and otherwise.
If you had evidence that this woman wanted to legislate that all other women to dress as she did, and that she was trying to limit their liberty by forcing them to do so, then yes, it would be clear she had committed an offense of some sort, and it would be reasonable to arrest her under whatever laws applied. (Though even then the laws of SA would not be relevant - it would be all about what was happening to French people on French soil.) But that is not what is going on here.