An injury-time touchdown from Damien Traille broke brave Scottish hearts in the opening RBS 6 Nations clash in Paris.
The battling Scots threatened to spring one of the biggest upsets in championship history when they turned last year's table upside down to lead 9-0 early in the second half.
But the out-of-sorts French gradually fought their way back and, after fly-half Yann Delaigue had levelled the scores with a 77th-minute drop goal, they pounced for the only try of the match in the third minute of stoppage time.
Hugo Southwell's attempted clearance five metres from his own line was charged down by Traille and the big centre was quick to gather the ball and stretch out for the match-winning score, although it needed the video referee to confirm it.
It was a cruel ending for Scotland, last year's wooden spoonists, who defied their critics and cast aside the domestic in-fighting which marred the build-up to the championship.
They produced a magnificent performance at a stunned Stade de France and looked to have provided coach Matt Williams with his first RBS 6 Nations win when full-back Chris Paterson kicked two penalties to give his side a 6-0 interval lead and stretched it to 9-0 with a third two minutes into the second half.
But the French gradually got their game together and, after missing with two first-half kicks at goal, Delaigue made it third time lucky after 50 minutes before adding a second to cut the deficit to just three points.
The Scots would have been delighted with a share of the spoils but even that was denied them in a frantic, heart-stopping finish which saw John Petrie sin-binned in the dying minutes.
Scrum-half Chris Cusiter produced a magnificent performance for the Scots, providing a constant threat in attack and working tirelessly in defence, and he deservedly won the RBS 6 Nations man of the match award.
France: Elhorga, Rougerie, Traille, Liebenberg, Dominici, Delaigue, Mignoni, Marconnet, Servat, De Villiers, Pelous, Thion, Bonnaire, Tabacco, Chabal.
Replacements: Valbon for Rougerie (18), Michalak for Delaigue (74), Bruno for Servat (80), Milloud for De Villiers (52), Lamboley for Thion (70), Nyanga for Tabacco (64), Yachvili for Valbon (80).
Scotland: Pens: Paterson 3.
Scotland: Paterson, Danielli, Craig, Southwell, Lamont, Parks, Cusiter, Smith, Bulloch, Kerr, Grimes, Murray, White, Hogg, Petrie.
Replacements: Douglas for Kerr (55), Hines for Murray (66), Dunbar for Petrie (80).
Not Used: Russell, Blair, Ross, Hinshelwood.
Before Will Greenwood started breaking down moves off the field, he was doing the business on it - and no match better illustrated the type of marauding centre he was than in a virtuoso performance against Wales.