Xan Mousques, Hoani Bosmorin, Thomas Souverbie and Mathis Castro-Ferreira all crossed in the first half at the Hive as Les Bleuets led 26-0.
But Scotland fought back in the second half, tries from Murdoch Lock and Jerry Blyth-Lafferty getting the home side back into it.
It was not enough to pull off an unlikely comeback, but Kenny Murray and his side will have taken a lot of heart from the performance of his team.
France had the first chance of the game, Joé Quere Karaba ripping the ball out of a tackle in his own half before racing more than 50 metres into Scottish territory. A desperate tap tackle from Isaac Coates denied him a stunning score.
Their first try was a fine effort though, Mousques receiving the ball 30 metres out before slipping inside two defenders and fending off another on his way to the line. Axel Desperes converted to make it 7-0 after 15 minutes.
That seemed to liberate France, and speedster Bosmorin finished a wonderful counter-attacking score. Good hands and straightening opened up the overlap, Patrick Tuifua sending his winger away. Bosmorin skipped away, cut inside and despite being tap tackled, bounced back up to evade two more defenders and get over. Desperes again converted.
The third try followed on the half-hour. France set up shop five metres out and after initially looking to maul, they shifted the ball back blind for Souverbie to slip through a tackle and force his way over.
Then right on the stroke of half-time, skipper Castro-Ferreira brought up the bonus point from close range, forcing his way over on a pick and go. Desperes converted from the touchline to make it 26-0.
Scotland responded well after the break and were rewarded for their efforts with a first try on 52 minutes. After forcing an infringement on the 22, Lock showed quick thinking by taking a tap with no French defence in the backfield, skipping through and over.
They were really on top and when Siale Tolofua dragged down a rolling maul, he was sent to the sin-bin. Scotland went back to the maul and there was no stopping them this time, Blyth-Lafferty getting the ball over the line.
That appeared to force France into a reaction, and they got up to the Scotland line before Fergus Watson failed to roll away, giving Desperes a simple shot at goal to make it 29-14 with quarter of an hour to go.
It was Scotland who finished the stronger, a couple of kicks for touch from penalties going dead when they could have set up more rolling mauls.
That meant that France were able to see out the game, Castro-Ferreira fittingly booting the ball out to secure the bonus-point win as France move up to third in the table ahead of a home clash with Italy.
Scotland, meanwhile, will now play host to England as they seek a first win of the campaign.