Born in Briançon, the son of a mountain guide, Luc started skiing when he was two years old.
He won his first high standard race at 11 and clinched the World Downhill Junior title in Sestriere in 1983.
However his career was plagued by injuries: a fractured wrist and torn thumb ligaments in 1987, an open fracture of the fibula in 1988, torn ligaments in the right knee in 1989 and broken vertebra in 1990. In 1993, he had a spectacular fall at Whistler Mountain in the USA ending up with a torn abdomen and detached knee ligaments.
Then in 1994 he won his first downhill at Val d'Isere and, in the winter of 1995, he won the two World Cup downhill races on the "Streif" run at Kitzbuehel in Austria.
He was ranked number one in the world in men's downhill in 1995 and 1996 and in 1997 he became the first Frenchman to win the overall World Cup since Jean-Claude Killy in 1968.
Alphand retired from skiing at the end of the season. He had already started racing cars in 1997 and raced in the Nissan Micra Stars Cup that year and 1998, when he also entered his first Dakar Rally.
He competed in the Dakar again in 1999, 2002 and 2003. In the 2004 race he finished fourth and in 2005 was the runner up.
He started competing in the European Le Mans Series in 2001 and the FIA GT Championship in 2002, along with the Lamborghini Supertrophy.
In 2006 he won the Dakar Rally.
In 2006 he aquired a Corvette C5-R from Pratt & Miller in Detroit for $1M to enter the 2006 Le Mans series.