Late on a Sunday evening a little more than a year ago, Marine Le Pen took the stage in a depressed working-class town in northern France. She had just lost an election for the region’s top office, but the leader of France’s anti-immigrant, anti-euro National Front did not deliver a concession speech. Instead, Ms. Le Pen proclaimed a new ideological struggle.

“Now, the dividing line is not between left and right but globalists and patriots,” she declared, with a gigantic French flag draped behind her. Globalists, she charged,...