Didier Deschamps' men headed into the game three points adrift of Group I leader Spain, and knew that victory would likely not be enough to see the team qualify automatically.
Franck Ribery gave France the lead with a superb finish from distance after just eight minutes, before Joona Toivio's own goal and Karim Benzema's late strike ensured triumph.
France dictated for the majority of the game in what was a strong performance, but the efforts proved in vain as Spain's 2-0 win over Georgia ensured that the world and European champion topped the group.
Deschamps made just two changes from the side that side that hammered Australia 6-0 on Friday as Blaise Matuidi and Mathieu Valbuena replaced Yohan Cabaye and Loic Remy.
The home team made a quick start to proceedings, Paul Pogba firing wide as Deschamps' men looked to seize the advantage early.
It did not take them long to find the opener as Ribery cut inside on to his right foot before firing a magnificent long-range effort in off the bar, leaving Niki Maenpaa helpless.
France showed great attacking intent in the first half, and only the reflexes of Maenpaa prevented the club from doubling the lead as he saved well to keep out Valbuena's header.
Finland was a danger on the counter, though, and France had captain Hugo Lloris to thank for preserving the lead, the Tottenham goalkeeper producing a fine stop from midfielder Kaspar Hamalainen one-on-one.
The visiting side looked to gain confidence from that near miss, and almost took the lead in spectacular fashion as Alexander Ring's improvised volley dipped just over the bar.
Still, Maenpaa was the busier of the two keepers, and demonstrated more wonderful reflexes to repel Olivier Giroud's point-blank strike after the Arsenal forward had latched on to Ribery's pull back.
France was almost made to pay for its profligacy early in the second half as Teemu Pukki shot wide following good link-up play with Hamalainen.
Deschamps' side found plenty of space in the Finland defense, however the club was once again thwarted by Maenpaa, who performed further heroics to parry Mathieu Debuchy's fierce drive.
The second goal did finally arrive after 75 minutes when Toivio turned Giroud's header into his own net after the striker had risen to meet Debuchy's fine right-wing cross.
Substitute Remy hit the post with a header, before Cabaye wasted a gilt-edged chance to score, but a third arrived three minutes from time as Benzema hooked home Ribery's left-wing cross.
France will discover its opponent in the playoffs when the draw is made on Monday.
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- Sports & Recreation
- Franck Ribery
- Didier Deschamps
- Karim Benzema
- Yohan Cabaye
- Joona Toivio