At the end of the civil war in Sri Lanka, Dheepan (Jesuthasan Antonythasan), a Tamil soldier, is seeking a way out. His family and comrades have been killed and he wants to start a new life. He meets Yalini (Kalieaswari Srinivasan) in a refugee camp. Together they create a fake family with young Illayaal (Claudine Vinasithamby), fool the aid workers and get to France.
Once in Paris, they must use their ingenuity to survive and make their fake family real. Dheepan manages to find a job as a caretaker in a run-down, crime-ridden building but past violence and new dangers combine to threaten their lives.