CHRISTIAN LOUBOUTIN, dressed in shorts, a faded navy T-shirt and a pair of well-worn yellow Havaianas, his straw fedora askew, is stretched out on an overstuffed banquette overlooking a rice paddy on Portugal’s Alentejo coast. The Paris-based shoe designer arrived here two weeks ago to sketch his next collection, something he does every season in seclusion. His compound of low-slung whitewashed bungalows is set off a dirt road outside of Melides, a beach village just south of the resort town of Comporta, which Louboutin used to frequent before it became a popular destination. “I received invitations to parties from people...