Travis Henderson walks alone through the West Texas desert in a fugue state, before stumbling into a building and losing consciousness. A German doctor examines him and determines he is mute, but discovers he possesses a telephone number and calls it. The call is answered by Walt Henderson, Travis’ brother from Los Angeles. Walt has not seen or had contact with Travis for four years, and agrees to travel to Terlingua, Texas, to retrieve him. His French wife, Anne, is concerned about the matter, as they have adopted Travis’ son Hunter, with Hunter’s biological mother Jane also missing. Walt reaches Terlingua, and finds Travis wandering from the clinic where he was found. The two brothers begin driving back to Los Angeles. With Walt becoming increasingly frustrated with Travis’ muteness, Travis finally utters the name “Paris”, asking to go there. Walt mistakenly assumes he means Paris, France. Farther down the road, Travis shows Walt a photograph of empty property in Paris, Texas, which he had purchased, believing he was conceived in that town.
The brothers reach Los Angeles where Travis is reunited with Anne and Hunter. Hunter, aged seven, has very little memory of his father, and is wary of Travis until the family watches home movies from days when they were all together. Hunter realizes that Travis still loves Jane. As Hunter and Travis become reacquainted, Anne reveals to Travis that Jane has had contact with her, and makes monthly deposits into a bank account for Hunter. Anne has traced the deposits to a bank in Houston. Travis realizes he can possibly see Jane if he is at the Houston bank on the day of the next deposit, only a few days away. He acquires a new vehicle and borrows money from Walt. When he tells Hunter he is leaving, Hunter wishes to go with him, though he does not have Walt or Anne’s permission.
Travis and Hunter drive to Houston, while Hunter recounts the Big Bang and the origins of Earth. When they arrive at the Houston bank, Hunter identifies his mother in a car, making a drive-in deposit. He calls for Travis via walkie-talkie, and they follow her car to a peep-show club where she works. While Hunter waits outside, Travis goes in, finding the business has rooms with one-way mirrors, where clients converse with strippers via telephone. He eventually sees Jane, though she cannot see him, and leaves.
The next day, Travis leaves Hunter at the Méridien Hotel in downtown Houston, with a message that he feels obliged to reunite mother and son, as he feels responsible for separating them in the first place. Travis returns to the peep show. Seeing Jane again, and with her seemingly unaware of who he is, he tells her a story, ostensibly about other people. He describes a man and younger girl who meet, marry and have a child. The man descends into alcoholism, while the young wife suffers from baby blues and dreams of leaving the family. The man also dreams of withdrawing to an unknown place “without language or streets”. A fire in the trailer home, after an incident of domestic abuse, finally parts the family. Jane realizes she is speaking with Travis, and that he is recounting the story of their relationship. He tells her that Hunter is in Houston and needs his mother. Jane has longed to be reunited with her boy, and that night, enters the hotel room where Hunter is waiting, while Travis watches from the parking lot. As Jane embraces Hunter, Travis climbs into his vehicle and drives away.