"You can't win the Six Nations in the first game but you can lose it.
"We ground out a good performance when there was potential for déjà vu from two years ago but the way we won that penalty at the end showed the hunger in the team."
O'Driscoll heaped praise on man-of-the-match and number eight Jamie Heaslip, who sides-stepped his way to the opening Irish try with a surging run.
"That boy has magic feet; I used to be able to turn like that but not any more," O'Driscoll said. "I don't think (Maxime) Medard even got a hand on him.
"It was brilliantly taken and a very well-worked team try.
Kidney pleased by Irish performance
"All the tries were very pleasing but the general performance and the attitude was what won it for us."
O'Driscoll's captaincy was questioned in some quarters prior to the Six Nations but the Lions centre played down the issue, as well as his individual contribution to Saturday's victory.
"You don't answer questions in one game. Maybe I have helped my cause a little bit.
"So much is made of the captaincy but there was incredible leadership throughout the team.
"It's not about what you say in the dressing room beforehand."
Coach Declan Kidney was able to celebrate ending a seven-game losing run against the French in his first Six Nations game in charge.
"Our defence was top class," said Kidney. "Our forwards were immense.
Someone asked me on Saturday morning was I nervous, and I replied 'no' which is rare
Fly-half Ronan O'Gara
"The French were a joy to watch. We had to be sharp to close them down and they just weren't going to get over our line.
"I am just delighted for the players. It's not about me. Someone has to be in the hotseat. Things went our way and some things did not go France's way."
Fly-half Ronan O'Gara, who kicked 15 points to move within four of the 900 mark in Test rugby, said Ireland "had the killer instinct in the backs".
"You could see the damage we did. It is a good starting point," he added.
"I just had a feeling throughout the week that something in the camp was different. Someone asked me on Saturday morning was I nervous, and I replied 'no' which is rare.
"I thought when we went 20-10 up that we would kick on but they came back at us. However, our new style game plan suited us."
Lock Donncha O'Callaghan believes the Irish no longer have anything to fear from the better resourced nations, such as France, and the victory over Les Bleus will add further momentum to their championship bid.
"Sometimes I don't like playing us down because we don't fear these teams any more," he said.
"Sometimes you can pay too much lip service to them and granted they have more players to select from, but we shouldn't play down to that.
"This win puts us in a great position in the Six Nations, even if we have played just one game.
"Winning's a habit and hopefully we can keep it going throughout the championship."
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