France overcame gutsy Scotland resistance to pick up their first win of the tournament but could not avoid finishing last in the Six Nations.
Greig Laidlaw kicked the visitors into a 6-0 half-time lead as the Scots defended like lions.
But French pressure continued to build and Wesley Fofana and Maxime Medard scored tries as tackles were missed.
Tim Visser responded with a late breakaway touchdown but Scotland could not manage a third campaign victory.
A third place finish is Scotland's best effort since 2006 and the competition will be judged positively, although many of the same failings remain.
On a cold, wet night in Paris, Scott Johnson's men were rarely seen as an attacking force.
Official match stats
Scrums won (lost)
Line-outs won (lost)
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In difficult conditions, both teams made several handling errors, while scrummaging was rendered close to farcical on a pitch that cut up badly under the studs.
Without a win in their last seven Six Nations games, the hosts were in a hurry to engage the crowd but found themselves trailing to two Laidlaw penalties after 18 minutes.
There followed a 10-minute period of intense attacking play from France, with recalled centre Mathieu Bastareaud regularly bulldozing his way forward.
However, Louis Picamoles, Sebastien Vahaamahina and Fofana were all stopped within inches of scoring as the Scots scrambled with great tenacity and a discipline that was missing in last weekend's loss to Wales.
Scotland managed one glimpse of a score when winger Max Evans, on for the injured Sean Maitland, broke two tackles in midfield and chipped into the French 22 but French full-back Yoann Huget beat him to the chase.
The half-time whistle brought loud jeers from the Stade de France audience as the battered visitors left the field gulping for air.
French playmaker Frederic Michalak made more mistakes than most in the first 40 minutes only to atone with three straightforward penalties in the first 13 minutes of the second period.
However, the moody fly-half can consider himself lucky to have still been involved as the match officials missed his cowardly off-the-ball punch on the back of Stuart Hogg's head.
France 23-16 Scotland: Reaction
The Scotland full-back immediately confronted his assailant and the pair were engaged in an ugly spot of grappling while play raged on.
The visitors looked weary but got back on level terms shortly before the hour mark, Laidlaw kicking another penalty following an offside decision.
French replacement prop Vincent Debaty then thundered down the left flank after crashing through a couple of challenges but he could not run over the top of Hogg and the home crowd wailed in horror as he failed to release the wide open Vincent Clerc.
The home attacks kept coming and Hogg did well to block Clerc as the stylish winger burst through the gain-line but the breakthrough was not long in coming.
Fofana broke free on the right and brushed off a weak Hogg tackle to touch down under the posts, with Michalak converting.
The French added a second try soon afterwards following a rumbling break by Bastareaud. Sean Lamont did well to down the powerful centre but the ball was quickly worked to Medard to slip through.
Replacement Maxime Machenaud converted as Michalak lay prone on the ground with a shoulder problem.
Evans and Visser broke tackles as the Scots rallied gamely and a promising attack broke down with a dreadful knock-on from substitute fly-half Ruaridh Jackson, who had started the move with a quicksilver pass.
Scottish bravery was rewarded when Matt Scott darted forward before playing in Visser who galloped away to score under the posts, with Jackson adding the extras.
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