PARIS—Peugeot struck a more than €2 billion ($2.1 billion) deal to buy General Motors Co.’s unprofitable European operations, a daring move by a French auto maker that is still early in its own financial recovery.

The deal, announced Monday, ratchets up Peugeot’s share of the growing European car market to 16%, passing French rival Renault SA for No. 2 in the region behind Volkswagen AG in terms of volume. The company officially known as Groupe PSA SA acquires the storied Opel and Vauxhall brands, Opel’s auto-finance operation...