What damage? First, Fox is a US corporation and not French. As such just how is Paris going to sue for insults? It has no legal jurisdiction. Second, as Dr. Pizza has said Fox is not accountable (nor is any other news agency) for what they did. Their opposite, MSNBC, would be sliced, diced, and fried if held accountable as virtually every other agency would if such lawsuits were allowed.
So this lawsuit isn't going anywhere and you really don't want it to do so whether you realize that or not. What will happen? Nothing. The overwhelming majority can be divided into three groups. First the Fox haters. They will always hate Fox, but probably have their own ideological favorites. Then there's the Fox followers, who will defend them and oppose the Fox haters and their sources. Those two groups occupy the opposite polar regions. Like our geographical polar zones there are relatively few who live there. The vast majority are in between and who are they? They are the "I really don't give a flying you-know-what" people. Almost no one cares about Fox or MSNBC and they certainly don't care about the wounded ego of Parisians, who the French themselves don't much care for.
There won't be any consequences. No one will change their minds about any of this. You'll love, hate or not care about this. For my part I'm glad it won't go anywhere, but not because of Fox, but because of the precedent it would set where governments worldwide could destroy the press so easily. I'm not a fan of that.