Born in Briançon (Hautes-Alpes), Alphand was world junior champion in 1983 and made his World Cup debut in 1984. It took a decade for him to make his breakthrough winning his first world cup at Kitzbühel 1995, and going on to take the overall downhill title 3 years in a row. In 1997 he won the World Cup overall title by collecting points only in the two speed disciplines, downhill and super G – a unique achievement in World Cup history. For this accomplishment he was voted L'Equipe Champion of Champions in 1997. The previous year he won a bronze medal at the 1996 World Championships at Sierra Nevada, Spain.
Overall he had 12 World Cup victories and 23 podiums.
Besides his outstanding skiing career, Luc has also engaged in motor sports. He participated in the Le-Mans race numerous times. But his highest motor sports achievement was to win the Dakar Rally in 2006.