It was the third defeat of Jones' 27 tests in charge and the Australian called for a sense of perspective while England address their slump.
"I don't think we should get too carried away or too melodramatic about where we are," he said. "We are a rugby team and no rugby team has an aura of invincibility about them.
"Every team is fallible and every team has a weakness and certain strengths and, at the moment, teams are outplaying us in certain areas of the game and we have to learn from it."
Maxime Machenaud converted four penalties and replacement first five-eighth Lionel Beauxis added another for the French, who were awarded a penalty try to break a 9-9 deadlock in the 49th minute.
It was the Tricolors' first win over England in four years in the championship, and a welcome respite. Just last month, they had gone eight matches without a win.
"I wanted the team to be close to the best during the tournament," France coach Jacques Brunel said. "We came close against Ireland, and this time, things turned out well for us. On both occasions, we were there."
The Grand Slam is on for Ireland on St Patrick's Day. The Irish stayed undefeated with a four-try bonus point at Lansdowne Road. It is Ireland's third championship in five years.
But the bigger prize would be beating England next Sunday (NZT) for Ireland to earn only a third Grand Slam, beside those in 1948 and 2009.
"We're going to have to save the best for last, and that's what it's going to take to win everything next week," Ireland captain Rory Best said.
"Everyone knows the size of the challenge. They haven't lost at Twickenham under Eddie Jones."
Scotland had their chances but weren't as accurate, and butchered at least two tries.
The bonus-point fourth try came with 11 minutes to go, when hooker Sean Cronin, only three minutes after replacing Best, dived over from the back of a rolling maul.
"We've a lot of big leaders," Best said. "At times when we were under pressure and they were trying to play chaotic rugby, we were able to get a breath back and get control through the spine of our team."
- AP