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What? I didn't know that... especially as it's rather European Arthouse Cinema, than Hollywood. Where did they film it then?

You're correct, it is a German/French production. From wiki

They filmed in West Texas in the desert. Paris, Texas is in East Texas about a 1000km away!

Paris, Texas, a real enough town, is the Godot of film locations. Lots of waiting, but it doesn’t actually turn up.
http://www.movie-locations.com/movies/p/paris.html

Nonetheless, an interesting film and not a typical Hollywood production ;-)