On Monday evening along Madison Avenue in Manhattan, while fashionistas on the Upper East Side finished their shopping rounds at Dior and Chanel, a crowd headed to the French Institute Alliance Française to attend the premiere of an Apple TV+ series that recounts the origin story of those two fashion houses through the tale of Coco Chanel and Christian Dior’s lives in war-torn Paris during the 1940s. “The New Look,” which starts streaming today, is a period drama that portrays the rivalry between Chanel, who is played by Juliette Binoche, and Dior, who is played by Ben Mendelsohn. The show...