Veteran striker Henrik Larsson and Lyon’s Kim Källstron both got on the scoresheet for Sweden with first and last goals of the game.
Larsson scored for Sweden after just six minutes with a spectacular shot at waist height before Benzema equalized on 19 minutes.
Two goals from Sidney Govou after the break gave the impression France would romp away with a goal spree, but Källstrom’s penalty five minutes before time gave the Swedes a more respectable scoreline.
Sweden had a number of scoring chances, exposing serious frailties in the French defence.
“That’s part of the game,” said French coach Raymond Domenech.
“If you want to push forward, open the game a bit more, play more freely, you give chances to your opponents.”