Giffords, who still uses a wheelchair much of the time, was on her first trip outside the United States since she was shot in the head by a gunman in January 2011 as she met local people outside a Tucson supermarket.
In bright sunshine but sub-zero temperatures at an altitude of 3,842 meters (12,605 feet) at the cable-car station on the Aiguille du Midi peak, Giffords smiled as she stood with her husband's arm around her shoulders.
"Gaby is really enjoying this visit," Kelly told friends and reporters. "This is a great day for us."
Kelly, accompanied by other U.S. astronauts, then visited a nearby mountain research station to install a plaque recalling the last U.S. space shuttle mission.
The trip was organized by Chamonix Tourist Office and the European Nuclear Research Centre, CERN, in Geneva, where the AMS particle detector, which Kelly and his Endeavour team took to the International Space Station in May 2011, was developed.
Giffords was a Democratic member of the House of Representatives but resigned her seat this January, saying her district deserved to have a representative "who can give 100 per cent to the job."
Six people were killed in last year's shooting, which was thought to have been an attempt to assassinate Giffords. She is undergoing intensive therapy and her speech is impaired.
(Editing by David Storey and David Brunnstrom)