Last December on the Côte d’Azur, guests at Lily of the Valley, a sea-facing wellness hotel near St. Tropez, sat outside on the sunny terrace having lunch. They were dressed in light sweaters and thin jackets. After 30 minutes in the warmth, a layer came off.

It was hard to imagine that London—a two-hour flight away—was being pummeled with rain. Though the French Riviera has become known as a summertime hangout, where super-yachts crowd the bays, it was historically a wintertime destination.