PARIS—French authorities arrested a key “yellow vest” protester for organizing an unauthorized demonstration, signaling a crackdown on a movement that has upended the agenda of President Emmanuel Macron.

Police held Eric Drouet on Wednesday evening near the Champs-Élysées, the glitzy avenue that has become a magnet for protests by the yellow vests—or gilets jaunes—over the past two months. He was leading a commemoration of yellow vests who have died since the movement began, mainly hit by cars inadvertently as they protested...