Aside from the fact that he made most of his money hosting infringing copies of American content, and serving ads to subscribers in the America, there was the more basic hook that he hosted some of the infringing content on servers in Virginia.
That's the problem most of the copyright infringement sites have. They deal primarily in content that is produced by Americans and considered a property right in America. The U.S. wouldn't give a shit if they were just trading foreign music and movies to each other. Even then, it was e.g. the Swedes that went after Pirate Bay (based on a criminal complaint filed by the MPAA in Sweden).
That seems essentially similar to the view of the French body here: if somebody somewhere harms somebody in our country, we can go after them, without regard to the law elsewhere.
