The French government seems to be engaging in a lot of useless roaring these days. Banning the Burkini was a senseless act that hasn't worked out as they had planned, and continuing on this road by threatening to press charges against social media users who post Burkini ban pictures is continuing down the same old dead end road.
The French government threatening to sue social media users who post Burkini ban photos is as laughable as the Cincinnati Zoo trying to get people to stop sharing Harambe memes. The country has no moral authority here, and any attempt to make such an attempt legal will rightfully be mocked by the rest of the world. It's amazing what lengths governments will go to try to restrict the speech of its citizens.
The quarrel over burkinis seems to have increased after a lady in a headscarf was pictured on a seashore in Nice getting rid of a long-sleeved shirt, and, at the same time, was flanked by law enforcement. France’s topmost courtroom seems to have overturned the latest prohibition on "burkinis" in the village of Villeneuve-Loubet, stating it turned out to be an obvious infringement of personal rights.
The reason why the French government has no legality in threatening to sue social media users is that social media is so widespread in society today that it would be impossible to track down every single user that has shared, posted, or re-posted said photos. Furthermore to try and sue citizens of outside countries would be an entirely messy and drawn out legal process that the French government simply cannot afford.