Don't Worry, I'm Fine (2006) on Netflix

Plot summary

Lili is nineteen and just back from Barcelona when she learns that Loïc, her twin, has gone from the family house without a word. She and her brother are close. He and their father argued violently before he left, and her parents refuse to tell her anything about it. The silence and the sudden absence wear her down; she stops eating, grows weak, and collapses in class. In the hospital she receives a letter from Loïc. He apologizes for leaving as he did and says he is traveling, living on petty jobs, and blaming their father for how his life has gone. The letter helps her begin eating again, and she recovers enough to return home. Believing her brother is living on the streets, she sets out to find him, following the letters.