In the 4-volume Robert's Dictionnaire culturel en langue française (2005), the word "pyreneism" is absent but nevertheless cited in the definition of "alpinism": Sport of mountain climbing (himalayism, pyreneism, [..], page 239.
If the word "alpinism", at least in France, gets detailed into andinism, himalayism,.. according to the massif in which the sport is practised, the cultural value of pyreneism in itself remains singular.