As said it's not an anti terror precaution, although the Nice Mayor is not defining it this way, he perhaps has another agenda. The ban, is seen as an extension to the burqa ban, the secular laws that France has, which also effect Jews, Sikh's and Christians, although only in government/public type places, buildings.I don't think it's an anti terrorism issue. More a drive to secularise France.
I also think it's probably a step too far, as if the burkini is not one of those full ninja suits, and just the common body suit with tight head cover, it's not a issues if they are down the beach just for a bit of pleasure like the rest of us. If they are following the husband around (you know what i mean), praying or preaching, doing the religious mumbo jumbo, then yeah, get them off the beach/fine them, although that would go for any religious nut really.