The USA are maybe the single nation with the most artistic contributions from foreigners, as i can't think of any other nation that was actually built in such a large part of foreigners, being that almost all of the former "Americans" were extinguished through a huge genocide  . Without european directors the USA would naturally be a much poorer film country. They were the ones that maybe did the most for US films, and influenced most US directors. Alone in my Top 10 of US films, I have 5 films directed by "foreigners", and in my overall Top 100 I have about 30 films that were directed by europeans. With Hitchcock and Chaplin we have even two giants of american film that came from Europe.


To add to both your lists:

Alfred Hitchcock: Vertigo, Notorious, The Birds, Rope.
Charles Chaplin: Almost everything
Mark Forster: Monster's Ball
Wim Wenders: Million Dollar Hotel (Paris, Texas isn't an american film!)
Douglas Sirk: Magnificent Obsession
James Whale: Frankenstein, The Bride of Frankenstein
Roger Michell: Changing Lanes
Billy Wilder: Sunset Boulevard, Five Graves to Cairo
Elia Kazan: East of Eden, On the Waterfront
Charles Laughton: The Night of the Hunter
Erich von Stroheim: Greed
Josef von Sternberg: Dishonored
William Wyler: Ben-Hur
Ernst Lubitsch. Design for Living
Stephen Daldry: The Hours
Andrew Niccol: Gattaca
Sam Mendes: American Beauty
Irving Rapper: Now, Voyager
Roman Polanski: Chinatown
Terry Gilliam: Twelve Monkeys, The Fisher King
Mike Figgis: Leaving Las Vegas
Michelangelo Antonioni: Zabriskie Point
Michel Gondry: Eternal Sunshine of the spotless Mind
Emir Kusturica: Arizona Dream

And Jonathan Glazer, Maya Deren, Jonas Mekas, Otto Preminger, Anthony Minghella were or are also Europeans.