French skiers occupied four of the top five places in their favorite discipline, topped by the 24-year-old from Nice who produced a swashbuckling second run to clinch his victory.
Hirscher, leader after the first leg, made a minor mistake and could not beat Faivre's overall time of two minutes 25.01 seconds, finishing just under half a second slower.
His consolation was taking the lead in the overall World Cup standings from Norway's Kjetil Jansrud, who had won both the super-G and downhill in earlier races at the French ski resort.
Jansrud crashed out on the first leg of the giant slalom in pursuit of a weekend hat-trick of victories.
Alexis Pinturault completed the podium, with fellow home competitors Thomas Fanara and Victor Muffat Jeandet in fourth and fifth.
France's Pinturault, who edged Hirscher in the opening giant slalom of the season in Soelden, is tied with him at the top of the discipline standings.
But the glory this time belonged to his compatriot Faivre, who said that off season training with his colleagues, who have the nickname the "attacking croissants", had boosted his confidence.
"It was a wonderful day, this is very special," he said.
Faivre, a former world junior champion, stepped up to the top spot after three previous podium finishes and is part of a growing French challenge in GS.
At least one of its racers has finished on the podium in 14 World Cup races since March 2015.
They will get the chance to extend that run on the same Val d'Isere slopes next weekend, with a giant slalom on Saturday and slalom Sunday.
Beaver Creek was due to stage the current round of racing, but it was switched to Val d'Isere because of a lack of snow at the Colorado resort.
Sunday also saw the return to World Cup action of last year's giant slalom overall winner Henrik Kristoffersen of Norway.
He has been involved in a dispute with his national federation, taking eighth on his return.
Olympic champion Ted Ligety of the United States was also off the pace in 11th place.