PARIS—Facebook Inc. is confronting a wave of probes in Europe into its privacy practices, escalating tensions between European authorities and a handful of U.S-based technology giants.

Government privacy watchdogs from France, Spain and Italy have in recent weeks joined a group of regulators investigating the social-networking company’s privacy controls, officials said, doubling the number of European countries analyzing the way Facebook handles the personal information and connections gleaned from more than 300 million users...