Ireland, who clinched only their second title since 1985, controlled most of the game, once again exposing France's paper-thin defence as Les Bleus finished the tournament in fourth place.
Flyhalf Jonathan Sexton scored two tries and kicked seven points as wing Andrew Trimble also touched down, while France's points came from Brice Dulin and Dimitri Szarzewski's tries and Maxime Machenaud's boot.
As the finish line beckoned, however, Ireland stopped playing and almost paid a fatal price when France scored a minute from time - only to have the ruled out for forward pass.
They survived the last minute to leave England second, on eight points but behind on points difference after thrashing Italy 52-11 away earlier on Saturday. Outgoing champions Wales finished third on six points following their record 51-3 demolition of 14-man Scotland.
"Je suis tres content," O'Driscoll said in French in a pitchside interview.
"It's a wonderful feeling. I've played a long time for Ireland and to only have won one Six Nations championship would have been disappointing so I'm really delighted for this group of players, for how talented they are, how hard they worked and to have won against a very good French team.
"This is fantastic, I'm so delighted to go out on this high, it's exactly as we would have wanted, to have a second Six Nations medal around my neck. I'm loving it.
"It's just a magnificent feeling. I'm sure there be a few tears later on and there were a few tears earlier when coach Joe (Schmidt) gave his last team talk. It was quite emotional.
"I promise you it's the last time in a green jersey. I'm absolutely overwhelmed. Huge emotions now, the last time I take this jersey off and hang it up inside, that'll be the end. Unless I decide to put one on at home when no one is watching."
Schmidt said: "The fairytale continued right to the end for the magic man (O'Driscoll) and I'm just delighted for him.
"It's unbearable, I'm not sure I can last too long doing this job, the heart just about gave up but I think we've shown incredible discipline right through the tournament and I think it was a credit to the players today that they maintained their discipline right to the finish."
They were 78,876 to attend O'Driscoll's farewell to international rugby after 141 appearances for Ireland and the British and Irish Lions and although he did not add to his record 26 championship tries, the centre was his usual battling self.
A simple win was all the visitors needed to secure their first tournament since 2009 but they had been hard to come in Paris for the Irish.
Machenaud put the home side ahead as Ireland were penalised early on, making it 6-0 after 15 minutes.
Ireland, however, worked through the phases and made the most of France's difficulties at the scrum, launching a well-constructed attack from a penalty for Sexton to touch down.
The visitors took control of the scoreboard midway through the first half after Conor Murray's defence-splitting pass set up Trimble, with Sexton adding the extras.
Shortly after the half hour, Huget knocked the ball down from Remi Tales's brilliant kick into the path of Dulin, who dived over to score France's first try.
Machenaud converted to give France a 13-12 lead.
Ireland missed a chance of regaining the lead on he stroke of halftime as Sexton missed a routine penalty.
France looked lively on the restart but Trimble was at it again, breaking down the right wing to set up O'Driscoll, who was tackled five metres from the line.
But Sexton, who had followed, touched down and converted to give Ireland a six-point lead, making it 22-13 minutes later with a penalty.
Somehow France surged back into contention after the Szarzewski was awarded a try despite knocking the ball on and referee Steve Walsh did not check the video replay.
Jean-Marc Doussain, who came in for Machenaud, missed a routine penalty with less than 10 minutes left but France still thought they had snatched it when Damien Chouly scored in the 79th - but the final pass looked clearly forward and the TMO agreed.
"Credit to Ireland - they are deserved winners and it's a fitting finale and send-off for Brian O'Driscoll, a legend of the game whom everyone in this squad respects massively," England coach Stuart Lancaster said in a statement."
While England can be pleased with their campaign, France have much to work on.
After a promising start to the championship with wins against Italy and England, they went off the rails in Cardiff when they were humbled 27-6 by Wales and never really recovered despite last weekend's fortunate 19-17 win in Scotland.
