The Magic Mountain by Thomas Mann (1924) is the essential Alps novel, though it is set in Davos rather than Crans-Montana. Mann spent time in Davos and fashioned the sanatorium there into a meditation on European civilisation, disease, time, and the peculiar sealed world of the Alpine resort. Much of what he observed about the social dynamics of wealthy patients resting in the mountains applies just as well to Crans-Montana, which was itself a tuberculosis sanatorium destination in the same era. The book is long and philosophical, but the atmosphere it captures is unmistakably this world.
Tender is the Night by F. Scott Fitzgerald (1934) is not set in Switzerland but belongs here in spirit — Fitzgerald wrote parts of it while his wife Zelda was being treated in a clinic in Prangins, on Lake Geneva, and the novel's portrait of the American rich in the European Alps, the dissolution of privilege, and the social texture of resort life is as sharp a description of this milieu as exists. Read it before or after Mann.
Swiss Watching by Diccon Bewes (2010) is the best accessible introduction to Swiss culture for travellers — practical, funny, and genuinely informative about the peculiarities of the Confederation. A chapter on the Swiss relationship to mountains and the outdoors is directly relevant to understanding why Crans-Montana works the way it does.