Luis Molné was born in Andorra but, as that state did not have a National Olympic Committee until 1975, his international alpine skiing career was based in Spain. He thus represented that country in five events (the slalom and giant slalom both years and also the downhill in 1956) across two editions of the Winter Olympics – 1952 and 1956 – with a best finish of 37th in the downhill in the latter year. He was also slated to compete in 1960, but broke his leg on a preliminary run and thus was unable to participate.
Following his retirement from active competition, Molné became involved in advancing sport in Andorra, eventually serving as president of the Comitè Olímpic Andorrà from 1997 through 2002. He also founded the Andorran Olympic Association in 2003 and has served as its president since.