David Steiner, 42, and Ornella Steiner, 51, both from the town of Bourgogne near Reims, had been hiking in the White Sands National Monument on Tuesday afternoon when they apparently died from heat exhaustion, Otero County Sheriff's Detective David Hunter said yesterday.
"They underestimated the elements," Hunter told AFP, adding that autopsy results were still pending.
Park rangers found the mother first while on a routine patrol. They checked her camera and saw that she had been with two other people, Hunter said.
Otero County Sheriff Benny House told local media that the family had been traveling across the United States, visiting national parks and monuments.
According to the Alamogordo Daily News, House said temperatures had been 38 degrees Celsius.
National Parks spokesman Patrick O'Driscoll told the newspaper there was no shade or water along any of the trails in the dune-filled White Sands National Monument.