The 2006 Alejandro González Iñárritu film that interweaves stories across languages and countries is Babel.
Written by Guillermo Arriaga, Babel follows connected characters in Morocco, Japan, Mexico, and the United States. Although the question describes three stories, the film is generally understood to contain four main storylines, linked by a rifle and by the characters’ unintended consequences for one another.
The film uses English, Spanish, Arabic, Japanese, Japanese Sign Language, and Berber languages. Its title evokes the biblical Tower of Babel and the difficulty people face when language, culture, and circumstance separate them. Brad Pitt, Cate Blanchett, Gael García Bernal, Adriana Barraza, and Rinko Kikuchi lead the ensemble cast.
Babel completes Iñárritu and Arriaga’s informal “Death Trilogy,” following Amores perros and 21 Grams. It premiered at Cannes in 2006, where Iñárritu won Best Director, and later won the Academy Award for Best Original Score for Gustavo Santaolalla.