I decided to look is there some more Georgian movies nominated for Oscar, and turns out one film prior to Tangerines actually was nominated, back in 1996 - A Chef in Love. I was a bit surprised to learn - that main role in this movie is portrayed by a very popular French actor - Pierre Richard.
A Chef in Love, (Georgian: შეყვარებული კულინარის 1001 რეცეპტი / Shekvarebuli kulinaris ataserti retsepti) is a 1996 Georgian film directed by Nana Dzhordzhadze. It stars Pierre Richard and Nino Kirtadze.
The movie tells the story of Pascal Ichak, a French opera singer and chef living in Georgia, who opens a restaurant. It also shows the life in Georgia in the beginning of the 20th century, including its short period of independence (see Democratic Republic of Georgia). After the Bolshevik coup attempt of Georgia (1920), the chef refuses to emigrate and endures the brutalities of the new regime.
The film was selected as the Georgian entry for the Best Foreign Language Film at the 69th Academy Awards in 1997. A Chef in Love was among the final nominees for the award, but did not win.
Update: I have removed link to this movie, instead you can acquire a legal copy in DVD format at Amazon: Shekvarebuli kulinaris ataserti retsepti