I think there are a lot of american movies that tell a story about a romance between a japanese and a foreigner. For japan movie I can only think about virgin snow (and it's really not my cup of tea), for the other movies, I watched these :
The drama Our House isn't super romance-y (probably more of a comedy-heavy romcom) but it's about an American woman and a Japanese man who get married and then she becomes the stepmom to his kids who then try to get rid of her.
The Secret Message (Japanese woman x Korean man) that this drama is primarily (probably 60-70%) in Korean so it's not realllly a jdrama. Still thought it was worth including!
There are also the Meitantei Catherine (usually spelled "Katherine" elsewhere) SPs. They're primarily mysteries but there's definitely a romance brewing between our titular heroine (played by Charlotte Kate Fox, who also stars in the abovementioned Massan & Our House) and her Japanese partner in sleuthing (played by Tanihara Shosuke).
In the romantic-comedy “Boku to Star no 99 Nichi” top Korean actress Han Yoo-Na (Kim Tae-Hee) falls in love with a quite man named Kohei Namiki (Hidetoshi Nishijima).
Kohei Namiki (Hidetoshi Nishijima) is a single man approaching his 40’s. He works at security company as a part-time job. He also has a sweet and handsome appearance, which some people take advantage of. Kohei is easily swayed by those around him. Kohei often takes care of his sister’s three kids because Kohei’s sister has a habit of wandering around, but he is a passionate man and dreams of finding his star. Because of his family and economic situations, Kohei can’t follow through on those dreams.