Les Bleus, who had lost three of their previous five Tests since securing the Grand Slam last March, quickly recovered their confidence following their 59-16 mauling by Australia last November to state their ambitions of retaining their title.
France crossed for tries through Maxime Medard, a penalty try, Imanol Harinordoquy and Damien Traille, with Morgan Parra kicking two conversions, Dimitri Yachvili two conversions and a penalty and Francois Trinh-Duc a drop goal.
The visitors were always chasing the game and Kellock and Brown's close-range tries followed by Lamont's late score - all converted by Dan Parks - were ultimately in vain as Scotland suffered defeat on the opening Six Nations weekend for the 11th time in 12 tournaments.
Scotland's most recent win in Paris had come on the way to victory in the final Five Nations Championship in 1999 and since the inaugural Six Nations tournament in 2000, Scotland had won their opening game just once - their most recent defeat of France, at Murrayfield in 2006.
Again Scotland return home from the French capital empty handed, looking to reclaim the momentum in next weekend's Test with Wales.
Exactly five years on from their last win over Les Bleus, when Kellock made his first Test start, Scotland were buoyed by victories over Ireland, Argentina (twice), world champions South Africa and Samoa in their last six Tests.
Kellock, who missed the autumn internationals following knee surgery, was one of three personnel changes - along with Nick De Luca and Max Evans - from the team which defeated Samoa.
Scotland had won twice in the French capital in 42 years prior to tonight's match and knew the opening 20 minutes would be crucial.
Head coach Andy Robinson called for his men to go toe-to-toe with their hosts but the optimism garnered from recent results was soon extinguished, with France's restored.
After three minutes De Luca was hit backwards in midfield and Thierry Dusautoir picked up the loose ball before feeding centre Aurelien Rougerie.
Rougerie kicked through and Medard sprinted outside Nikki Walker to win the race to touchdown. Parra converted.
Trinh-Duc added a simple drop goal from 15 metres after 10 minutes to leave the visitors trailing 10-0.
Scotland responded, taking the direct route. Richie Gray, Rory Lawson, Kellock and John Barclay made ground, the openside flanker caught three metres short.
However, from the resulting ruck, Kellock burrowed over, Parks converting to make it 10-7.
Scotland, though, were immediately back defending their own goal-line.
Referee Wayne Barnes penalised Scotland repeatedly at the scrum and, with tighthead prop Euan Murray under pressure from France loosehead Thomas Domingo, the hosts continually opted to reset and utilise their eight-man shove.
Number eight Harinordoquy again was dribbling forward with the ball at his feet as the Scotland scrum disintegrated once more, Barnes awarding a penalty try which Parra converted.
Scotland had a 10-point interval deficit to overhaul, with Mike Blair on for Lawson at scrum-half.
Parra dragged a long-range penalty wide as France missed the opportunity to stretch their lead.
Yachvili replaced Parra and prop Nicolas Mas came off for Luc Ducalcon, but France still had the impetus.
Blair kicked through after Scotland turned over the ball, but it merely allowed the hosts to run the ball back.
Trinh-Duc passed through his legs following a misplaced pass and Harinordoquy cut inside Gray and raced 40 metres in under the posts. Yachvili converted. It was Harinordoquy's last act of the contest as Sebastien Chabal replaced him.
Scotland then applied pressure on the French line and were awarded a penalty for offside.
Scotland opted to run the ball and were rewarded as Brown found a gap to score wide on the right.Parks added the extras.
France, though, scythed through the Scotland defence once more, Trinh-Duc racing down the left before moving the ball infield with Damien Traille going in under the posts.
Yachvili converted to hand France a 16-point lead with 10 minutes remaining.
Sean Lamont, a replacement for De Luca, latched onto Joe Ansbro's short ball to go in under the posts for Scotland.
Jackson converted to make it a 10-point game with three minutes remaining but France again exerted forward pressure and won a penalty which Yachvili stroked over to seal the win.