A brilliant bicycle kick by Sweden's inspirational captain Zlatan Ibrahimovic yesterday in the 54th minute gave them the lead with the outstanding Sebastian Larsson adding a second in the final minute of normal time.
It handed the Swedes not only their first points of the group stage but also their first win over France in almost 43 years dating back to October 1969.
The French, who also saw their 23-match unbeaten run ended, progress in second place in the group after England beat co-hosts Ukraine 1-0 in the other game to finish top.
France - who last reached the knockout stages of a major finals in the 2006 World Cup - will play champions Spain in the last eight.
The Swedes should have gone ahead in the eighth minute as Ola Toivonen - who had replaced the injured Johan Elmander up front - was played onside and with only Hugo Lloris to beat. However, although he rounded the goalkeeper he found the angle too tight and his shot hit the post.
The French pressed from the start of the second-half with Karim Benzema finding some space and curling the ball just past the far post. However, instead of sparking the French into some urgency it prompted the Swedes into their best period of play with Lloris pulling off one fine save in the 53rd minute.
A minute later he was unable to do anything about Ibrahimovic's stunning bicycle kick from Larsson's superb cross -- Ibrahimovic in typical celebratory style standing stock still and raising his hands pointing a finger of each hand at the sky.