No need for that; EU can essentially poison EU markets for FB (sanctions/fines/blocks). Most shareholders will act accordingly and tank the stock. Even if Mark can ignore because he holds most of the voting interest, this directly impacts all vested workers, so becomes an HR nightmare.
Why not do both? It would be so much fun - Facebook execs too scared to got to fly the jet to Europe for fear of being cuffed when they land.
The reality is facebook would happily pay the fine and the real loser would be the US taxman - in response the US would drum up some more "fines" against some European companies as payback. All of this has happened before, and it will all happen again.
Given that this is related to terrorism[1] I'm pretty sure a creative government could find a way to attempt penal prosecution here if they really wanted though (After the terror attacks in France in 2015-2016, French law made “terrorism apologism” a crime for instance, which is a scary law tbh, especially when we've seen how it was applied).
[1] I personally don't like to talk about the Hama's massacre as “terrorism”, as an organized military crossing a border to systematically eradicate civilian population is much more than terrorism: it is genocidal in essence.