Hope Powell's players - finalists four years ago - needed a win at the Linkoping Arena to guarantee their progression from Group C but an early goal and a second-half double condemned them to an early flight home.
Eugenie Le Sommer had ominously rattled a post with only eight minutes gone but swiftly went one better, rewarding Elodie Thomis's swashbuckling run with a low finish into the corner.
England pressed and harried higher up the field but though France were restricted to long-range efforts as the first half drew to a close, Louisa Necib's drive needed a firm palm from Karen Bardsley.
Powell replaced Anita Asante with attacking midfielder Jill Scott after the break but Thomis continued to exploit gaps further back, threatening to finish a clever Necib through-ball, before blazing one shot wide.
Toni Duggan had fired over the French goal after a rare attack at the other end but a quickfire double killed the contest - just moments after barely-fit talisman Kelly Smith was desperately thrust into the fray.
Necib found space to twist and hook the ball past Bardsley (62), before delivering a corner that Wendie Renard rose to meet two minutes later.
Thomis might have grabbed a fourth goal with a dragged effort 20 minutes from time but Bruno Bini's side had long secured their quarter-final spot.
Powell felt a pre-season declaration that failure to qualify from the group would be "a disaster" had come back to haunt her - but insisted she was the right woman to lead a World Cup qualifying campaign this autumn.
The Londoner, whose side had previously slipped up 3-2 to Spain before salvaging a last-gasp draw with Russia, told the BBC: "I said it would be a difficult task. France and Spain were difficult but we should perhaps have done better against Russia.
"We know we didn't play our best but big credit must go to France. They've got very, very good strength in depth.
"I have to regroup, the players have to regroup and go again. I don't like losing and we'll be back. More importantly the players will have learned some lessons and I'll have learned some lessons. We have to do better next time."