Ribery, an own goal and Karim Benzema put France on 17 points but victory proved academic with Spain, who finished three points clear, overcoming Georgia 2-0.
France, 25th in the latest FIFA standings which will be updated on Thursday, are unlikely to be seeded in the playoff draw which takes place in Zurich on Monday.
The hosts went ahead after eight minutes when Ribery, a hot candidate for the FIFA Ballon d'Or award after another impressive showing, unleashed a missile from the edge of the area that flew into the top corner.
Les Bleus, however, were shaky at the back at times with left back Patrice Evra put under pressure.
In the 19th minute, Kasper Hamalainen beat the offside trap for Finland but his weak shot from inside the box went just wide.
France missed several clear chances but put the result beyond doubt in the 76th minute when Joona Toivio deflected Olivier Giroud's header into his own net.
Karim Benzema, who ended a 15-game goal drought for France in last Friday's 6-0 hammering of Australia in a friendly, volleyed in from Ribery's fine pass to make it 3-0 three minutes from time.
(Reporting by Julien Pretot; Editing by Justin Palmer)
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