Miriam Besson and Antoine Besson are a divorced couple. They have a daughter close to the age of eighteen, Josephine, and an eleven-year-old son, Julien. Miriam wants to protect her son and keep him away from his father, whom she accuses of committing acts of violence. Therefore, during the trial, she asks for the exclusive custody of the child, above all because Julien himself doesn't want to see his father again. Despite Miriam's arguments and a letter from Julien, the judge responsible for the case grants shared custody and forces the child to spend the weekends with his father. Julien only wants to protect his mother from the physical and psychological violence inflicted by Antoine. Antoine wants to continue to exercise his power over Miriam and Julien with pressure and threats to the child, an attitude that makes Antoine hated by his own parents who decide to chase him away. Antoine intimidates Julien into showing him where the family has moved to. At Joséphine's 18th birthday party, Antoine comes back and, in order to find out Miriam and Julien's new address, he tries to immobilize his ex-wife by holding her throat, until she is saved in extremis by her sister Sylvia, who threatens Antoine to call the police if he ever shows up again. One night, while Miriam and Julien are sleeping at their home, Antoine tries to enter the apartment, armed with a rifle. A neighbour calls the police. Miriam and Julien barricade themselves in the bathroom and call the police who arrive and manage to disarm and arrest Antoine before he can kill anyone.
On review aggregator website Rotten Tomatoes, the film has an approval rating of 95% based on 115 reviews, with an average rating of 7.8/10. The website's critical consensus reads, "Custody uses formal restraint — and a series of searing performances — to take a hard-hitting look at the often painful bond between parents and children." On Metacritic, the film has a weighted average score of 83 out of 100, based on 21 critics, indicating "universal acclaim", and is listed as a "Metacritic must-see". For The Canadian Press, David Friend said, "Xavier Legrand captures unsettling performances from his entire cast, especially the young Thomas Gioria as the child caught in the midst of turmoil." Peter Rainer of Christian Science Monitor noted "the ordeal of the children is not skimped. They bear the brunt, and the legacy, of the anguish."
