The son of 2002 Olympic slalom silver medallist Sebastien Amiez finished in 47.44 seconds, 0.32sec ahead of Norway's Henrik Kristoffersen who is looking to extend his lead at the top of the discipline and overall standings.
Austria's Manuel Feller was third-quickest, 0.66sec behind the 26-year-old Amiez.
"It's cool to cross the finish line and see the green light on and hear the crowd screaming," said Amiez who finished sixth in the first slalom of the winter in Finland's Levi before taking fourth place in Austria's Gurgl last month.
"I'll try to do the same in the second run. I've already been in this position in lower level races so I don't see why it would change anything.
"It's still a track with snow and poles, so we'll have to do the same."
Another Frenchman, the Olympics slalom champion Clement Noel, decided not to race after suffering a heavy fall during Saturday's giant slalom.
"I went to try (to ski) the warm-up run and I saw that it was impossible," said Noel who was aiming for a third consecutive slalom victory this season.
"I can't press. I don't dare. It really hurts when I press on my leg, so there was no point in taking any unnecessary risks."
Noel took a gate head-on during the first run of the giant on Saturday and finished his race in the nets. He was able to ski back down but broke several teeth and sprained his right ankle.
He is now targeting a return to the piste in Alta Badia, where the next World Cup slalom takes place on December 23.
The second run at Val d'Isere starts at 1200 GMT.
