city of lost children and amelie are not independant films, they're french.
My suggestion is imdb.org. Search by director. The same guy that made COLC and Amelie made and a great flick called delicatessen. Another great director to check out is julio medem. The guy makes awesome films. Of particular interest is sex y lucia and perhaps Amantes del Círculo Polar. While you're checking out spanish cinema, try intacto (freshman film of fairly high caliber). Real independence is something more like David Lynch. See also: Lost Highway and Mullholland Drive. In the foreign vein, you should watch all of wong kar wai's stuff. He's a masterfull artist. Requiem actually stole a huge amount from one of the segments of his "chungking express". His best includes "Fallen angels" and "Ashes of Time". Damn he's good -- See also: Sunzhou River. Next detour is japanese horror. Hideo Nakata more or less recreated the scene with ringu. That's the classic, but "Dark Water" is by far his best. After that give "Chaos" a try. Zipping back to france, Irreversible is a really awesome anachronistic flick (gets a bit graphic at times). The Piano teacher is also quite entertaining in the perverse french way. Back to america, the Coen brothers give you "Barton Fink" and also "The man who wasn't there" (my personal favorite).
Have fun-