ANTIBES, France — In a matter of minutes, torrential rains transformed the postcard-perfect French Riviera into a terrifying flood zone, leaving at least 16 dead, trapping hundreds of ailing pilgrims and halting car and train traffic Sunday along the mud-drenched Mediterranean coast. Residents, stunned by the ferocity of the brief downpour Saturday night, described it as the worst flooding they’d ever seen — so dramatic that President Francois Hollande paid an emergency visit Sunday to promise government aid for victims. Helicopters patrolled the area and 27,000 homes were without electricity Sunday after rivers and streams overflowed their banks and fierce thunderstorms poured more than 6.7 inches of rain in Cannes and some other areas, according to the Interior Ministry. Government officials gave conflicting reports about casualty figures throughout the day, as emergency services fanned out across the region to check homes, stores and overturned cars for victims.