France captain Rafael Ibanez said winning the Six Nations title was proof of his side's winning mentality after the setback of losing to England.
Ibanez finally got his hands on the trophy after England lost
Their 46-19 win over Scotland ended Irish hopes of winning the title and France were confirmed as winners when England lost 27-18 to Wales.
"After last week against England, we showed some character here," he said.
"This was important. I'm not sure it'll mean anything for the World Cup but we played well and won - that is good."
I am stunned, even dazzled by the way the team played
France coach Bernard Laporte
Ireland's 51-24 win over Italy meant France had to beat the Scots by 24 clear points to knock them off the top of the table.
Elvis Vermeulen's last-gasp try ensured they won by 27 points, and meant only a crushing England win over Wales in Cardiff could deny them the title, but as it turned out Wales won that match.
"The days after our poor game against England were tough and the news of the Ireland score was another blow but we showed a lot of character," said Ibanez.
"We were mindful of their result. We knew what we had to do. But it was not a conventional match format.
"We tried to build our victory one step at a time. We got off to a bad start, but we tried to free up our playmakers from then on.
"We have guys in that team who proved today that they are true champions."
France coach Bernard Laporte, who was taking charge of his last Six Nations game, said: "I am stunned, even dazzled by the way the team played and managed to hold themselves together, especially at the end.
"It is a culmination of a whole week of hard, hard work. I commend the mindset of our players.
"It was one of our best matches for a long time, although there is no such thing as a perfect match.
"We started to gain positive momentum, and the attitude of the players made the difference.
"The crowd were great as well. The public are ready for the World Cup - they were on the same wavelength as the players."