AMIENS, France — Two Goodyear managers held captive by angry French workers were freed Tuesday after police intervened, ending a two-day standoff over the factory’s bleak future.

The release outraged union members, who made a bonfire of tires in front of the plant. It also left unresolved the larger problems that have dogged the plant in Amiens in northern France, which Goodyear has tried to sell or shutter for more than five years.