Gael Fickou gave the defending champions a bonus point with a last-minute try to add to those of Romain Ntamack, Ethan Dumortier and Thomas Ramos, who kicked the rest of the points.
Scotland, who defended ferociously and came close to overturning a 19-0 deficit, scored with two tries from Huw Jones and the boot of Finn Russell, who also added a try as the visitors recovered from a woeful start.
They had lock Grant Gilchrist sent off after seven minutes, six minutes before France prop Mohamed Haouas was also shown a red card.
Fabien Galthie's side were looking to bounce back from their defeat by Ireland, their first in their last 15 tests, and while they managed to get back to their winning ways, they did not appear as invincible as in 2022.
Scotland, after wins against England and Wales, will now look to stay in contention for the title when they take on unbeaten Ireland while France will travel to England.
"We have not let the trophy go yet," said Galthie after the result left France on 10 points, behind Scotland and England on points difference and five points adrift of leaders Ireland.
"We felt like we could win that. After a really tough start, we got back into it, had ascendancy in the second half. We couldn't get over the line in the last 10 minutes," Scotland's Jones lamented.
Les Bleus went through the phases early on and Ntamack touched down wide after the forwards had worn down the Scottish defence.
Gilchrist then made a direct shoulder contact with Anthony Jelonch's face and was sent off after referee Nika Amashukeli saw a "high degree of danger" in the move.
RISK-TAKING
Dumortier went over shortly afterwards on the from the left wing to put France 12-0 up, only for Haouas to be shown a red card in the 13th minute for a head-first charge at Ben White's head.
It spurred Scotland into action, but Les Bleus were more clinical as Ramos intercepted a long pass from Russell in for the hosts' third try after a 50-metre run.
Russell was more inspired to put the visitors on the scoreboard with a superb pass for centre Jones who touched down between the posts.
While Scotland remained a constant danger with powerful driving mauls, Ramos added a penalty to give France a 15-point halftime lead.
Scotland reduced the arrears early on in the second half as Jones powered through for his second try as France's strategy was to limit the damage.
Some brilliant moves, however, brought Dumortier on the cusp of a fifth try for France, but the winger made a poor choice in front of the line.
Russell then dived over after a series of five-metre scrums to put Scotland within touching distance before France increased the pressure in the final minutes, although they failed to make their domination count.
It was, however, France who had the last laugh with a risk-taking choice as they went for a bonus try, which Fickou got after being set up by Antoine Dupont in a final move that also denied Scotland a defensive bonus point.
