Didier Deschamps' men headed into the game three points adrift of Group I leaders Spain, and knew that victory would likely not be enough to see them 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 their efforts proved in vain as Spain's 2-0 win over Georgia ensured that the world and European champions 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 hosts made a quick start to proceedings, Paul Pogba firing wide as Deschamps' men looked to seize the advantage early.
And 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 them from doubling their lead as he saved well to keep out Valbuena's header.
Finland were a danger on the counter, though, and France had captain Hugo Lloris to thank for preserving their lead, the Tottenham goalkeeper producing a fine stop from midfielder Kaspar Hamalainen one-on-one.
The visitors looked to gain confidence from that near miss, and they 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 were almost made to pay for their 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 defence, however they were 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 their opponent in the play-offs when the draw is made on Monday.
|Coach: D. Deschamps|
for B. Matuidi 70'
for S. Nasri 71'
for O. Giroud 81'
|Milligan: Socceroos wary of Tajikistan|
|Conte wants more players like Pelle|
|OFC World Cup Qualifying Review: Samoa to meet Tahiti in next round|
|Krychowiak stayed at Sevilla because of Emery|
|I never considered Bayern exit - Gotze|
|Balotelli ´not in good condition´, Milan must improve - Mihajlovic|
|Robben slams ´stupid´ Martins Indi|
|Robben laments injury blow|
|Euro 2016 Qualifiers Review: Bale edges Wales closer, Iceland dent Netherlands´ qualification hopes|
|De Bruyne relieved to ´boss´ Bosnia-Herzegovina|
|Blind furious after nightmare debut|
|Coleman sees shades of Charles in Bale winner|
|Conte only concerned about Italy winning|
|Mauritania v South Africa: SAFA to investigate Masilela no-show|
|AFC World Cup Qualifying Review: Qatar hit 15 in Bhutan rout|
|Belgium 3 Bosnia-Herzegovina 1: De Bruyne shines in straightforward victory|
|Cyprus 0 Wales 1: Bale winner takes Wales one step closer|
|Netherlands 0 Iceland 1: Sigurdsson winner caps difficult first game for Blind|
|Italy 1 Malta 0: Pelle spares wasteful Azzurri|
|Balotelli stars in Milan friendly win|
|Bhutan thrashed 15-0 by Qatar in qualifier|
|Rwanda v Ghana: Gyan doubt gives hosts hope|
|Tanzania v Nigeria: Enyeama out of AFCON qualifier|
|Valdes and Berahino included in Premier League squads|
|Costa Rica v Brazil: Dunga´s men return after Copa disappointment|
|Spain v Slovakia: Azpilicueta eyeing important revenge|
|Adebayor left out of Tottenham squad list for league and Europe|
|San Marino v England: Place in history books beckons for Rooney|
|Germany can cope with Reus absence - Low|
|Bayern offer aid to refugees in ´training camp´|
|BREAKING NEWS: Welbeck ruled out for months after knee surgery|
|South Korea 8 Laos 0: Son leads the way in rout|
|Australia 5 Bangladesh 0: Socceroos surge to emphatic win|
|Japan 3 Cambodia 0: Hosts pick up first qualifying win|
|Rudiger aiming to nail down Euros spot after Roma move|
|Melo happy to join Inter at last|
|Hernandez thanks Ferguson after United departure|
|Chung: AFC has compromised FIFA election|
|Wales the new best of British|
|Reus out of Germany qualifiers|
|Chile v Paraguay: Vidal missing for Copa champions|
|Ghedin: Anything is possible for Malta|
|Pogba will be worth €100m - Marotta|
|England can win Euro 2016 - Hodgson tells players|
|Conte unsure over Balotelli future|
|Portugal - France Preview: Deschamps aiming to correct mistakes|
|Martial never the same again - Mangala|
|Copa del Rey Review: Racing fall at the first|
|Shelvey dismisses talk of England snub|
|Galatasaray unable to play Grosskreutz|
|Faroe Islands v Northern Ireland: O´Neill preaches patience ahead of Euro double-header|
|Levy slams ´wholly inappropriate´ West Brom after Berahino chase|
|Panama v Uruguay: Visitors without Suarez and Cavani|
|Captaincy won´t change me - Robben|
|Liverpool sign Brazilian youngster Allan|
|PFA expects swift Berahino resolution|
|Argentina v Bolivia: Mascherano backs ´very special´ Messi|
|´I do not know if I´m worth €80million´ - Martial shocked at price-tag|
|Afellay suspension reduced|
|Noble red card rescinded|
|Portugal v France: Deschamps aiming to correct mistakes|
|Bahebeck given the all clear|
|Germany v Poland: Muller out to settle the score|
|Gibraltar v Republic of Ireland: Keane counting on McCarthy and Walters|
|Georgia v Scotland: Tbilisi trip has must-win feel for Robertson|
|Juve still the team to beat - Hernanes|
|De Gea will remain professional, says team-mate Mata|
|Berahino given extra time off following strike tweet|
|´No excuses´ as Costa seeks to kick-start season|
|I´m not like Messi or Ronaldo – Hazard|
|United States v Peru: Klinsmann out to ´prove a point´|
|Martinez unsure when Cleverley will return|
|France set for Russia friendly ahead of Euros|
|Former Manchester United forward Berbatov joins PAOK|
|De Gea must play to earn Euro 2016 spot – Del Bosque|
|Cahill thrilled to lead Socceroos|
|Wijnaldum urges patience with new-look Newcastle|
|Reid praises Stones´ professionalism|
|Mexico v Trinidad and Tobago: Islanders hoping to build on Gold Cup display|
|Choosing Brazil over Spain was easiest decision, says Rafinha|
|Galliani hails ´changed´ Balotelli|
|OFC World Cup Qualifying Review: American Samoa notch second competitive win|
|Canada v Belize: Hosts look to stay calm|
|Carragher surprised by ´big´ Martial price|
|No pressure on Rodgers - Rush|
|No Benzema, no Cavani - Arsenal ´can´t compete´ says Sol Campbell|
|FFA muzzle Postecoglou after pay dispute criticism|
|Celtic complete Simunovic signing|
|Joaquin: I´m as happy as a little boy|
|Navas given time off by Costa Rica|
|Martial unfazed by prospect of United pressure|
|Ramos urges De Gea to overcome transfer woe|