Obviously will we just use the generally accepted notion of "foreign film" here. (Since yes US films are technically foreign films for our UK posters, etc...)
There clearly will be cross-over since folks could easily talk about Train to Busan or Under the Shadow here or in horror
For a starting point - Academy Awards nominations 2010-2014
2010
In a Better World (Winner)
Biutiful
Incendies
Hors la loi (Outside the Law)
Note: Dogtooth was also nominated but that is considered 2009 by IMDB
2011
A Separation (Winner)
Rundskop (Bullhead)
Hearat Shulayim (Footnote)
In Darkness
Monsieur Lazhar
2012
Amour (Winner)
Kon-Tiki
No
A Royal Affair
Rebelle (War Witch)
2013
La grande bellezza (The Great Beauty) (Winner)
The Broken Circle Breakdown
Jagten (The Hunt)
The Missing Picture
Omar
2014
Ida (Winner)
Leviathan
Tangerines
Timbuktu
Relatos salvajes (Wild Tales)