Spain also reached the quarter-finals with a 1-1 draw against Russia, who missed out on a place in the last eight when Denmark went through instead after lots were drawn.
The Russians were level with the Danes on two points but, with Iceland's four points clinching one of two spots available for the best third-placed teams, lots decided the final place.
Denmark face a daunting task in the knockout stages on Monday when they will meet a French side that dominated Group C ahead of runners-up Spain who will play Norway later that day.
Hosts Sweden face Iceland in the first quarter-final on Sunday before seven-times champions Germany take on Italy.
France outclassed England from the kickoff in Linkoping in their final group game, and Eugenie Le Sommer had already hit the post before she opened the scoring in the ninth minute.
Winger Elodie Thomis made a powerful run before passing to Le Sommer, whose strike beat England goalkeeper Karen Bardsley.
Le Sommer turned provider on the hour, feeding Louisa Necib, who curled a beautiful shot into the top corner beyond Bardsley.
When Wendie Renard headed home a corner for France two minutes later, England, who finished bottom of the section with one point, were heading for the exit.
In Norrkoping, Veronica Boquete gave Spain the lead early in the first half, but Elena Terekhova struck from the edge of the area to put Russia back on level terms just before halftime but there was to be no reprieve for the Russians who now head home.
(Reporting by Philip O'Connor; Editing by Steve Wood and Ken Ferris)
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