The boy landed with his grandmother at Charles de Gaulle airport in Paris Sunday as it emerged that his tourist parents may sacrificed their own lives to save his.
Otero County Sheriff Benny House said the boy was found dehydrated but responsive near the body of his father in the White Sands National Monument on Tuesday.
Rescuers found two empty 20-ounce (0.6-litre) water bottles close to the bodies.
"The father and mother would take one drink while they made the child take two swallows of water," House told the Alamogordo Daily News.
House said the boy told authorities that his mother had headed back toward their car after becoming ill. He carried on with his father.
Park rangers found the mother's body on a routine patrol of the area where temperatures had been reportedly been between 100 and 101 degrees Fahrenheit (38 degrees Celsius).
It was only when they checked her camera and saw that she had been with two other people, Hunter said, that a search began for the boy and his father.
David Steiner, 42, and his wife Ornella, 51, from the small town of Bourgogne near Reims in northeastern France, had been on holiday in the southwestern state when tragedy struck.
Their son arrived back with his grandmother on a British Airways flight late on Sunday afternoon, an airport source told AFP.
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