I don't know the context in which the GlobalDisplay instance is used well enough, but I'd either use some kind of lazy initialization method (like a Singleton), or have the user call an init() function manually, like SDL does. The latter would be my preferred route, although I'm a aware that's it's slightly opposed to the way your API is designed. I'd be happy with the Singleton, as long as it's a private interface, just the way it is now. One of the most basic C/C++ idioms should apply here, "you don't have to pay for what you don't use".
To fix the X11 stuff, I suggest a shutdown() function, which is responsible for destroying all SFML instances which are still alive. This is probably hard to implement in a clean way, but it would give users a surefire way to force all system calls to complete just before the end of main(), and to avoid the undeterministic static deinitialization mayhem.
Hopefully that did make sense...
