Jean-March Doussain's 78th-minute penalty saw France clinch a 19-17 victory at Murrayfield after Duncan Weir's penalty on the hour mark appeared to have done enough for Scotland.
Earlier, Scotland led through first-half tries from Stuart Hogg and Tommy Seymour but Yoann Huget's interception try and 11 points from Maxime Machenaud had put France 16-14 up on 46 minutes.
It was far from a vintage France performance but it puts Les Bleus second in the table to Ireland, courtesy of earlier victories over England and Italy.
Unless Wales and England draw on Sunday, France will slip behind the winner and down to third on points difference but with the Twickenham clash expected to be tight, Saint-Andre's side will know a win against Ireland next week could feasibly earn them the title.
"I think fair play to Scotland," he said. "They played very well and with a lot of spirit. They scored good tries in the first half.
"In terms of the game we managed to win - I can't say it was our best game.
"First half we arrived two or three times close to the line, but we wanted to score too quickly. We tried the silly or impossible pass. We need to improve our lineout.
"Now we prepare for a big game with Ireland next week at the Stade de France.
"I hope [Brian O'Driscoll's] party was today in Dublin and not next week in the Stade de France."