BRUSSELS—The European Parliament on Tuesday lifted the immunity of the former president of Spain’s Catalonia region, Carles Puigdemont, and two of his associates, a move that could pave the way for their extradition and reopen the scars of separatism in Spain.

Member of European Parliament Carles Puigdemont prepares for an interview at the European Parliament in Brussels, on March 9, 2021. Francisco Seco/AP Photo