Ronan O'Gara opened the scoring with a 2nd minute penalty before Imanol Harinordoquy scored a try in the corner that Lionel Beauxis converted. O'Gara landed a second penalty, missed with a third effort and then added the points to Heaslip's 33rd minute try.
Beauxis landed an injury time drop goal to leave France trailing 13-10 at half time.
Two minutes after the restart O'Driscoll slalomed through off a flat O'Gara pass but Maxime Medard then collected a beautiful Beauxis kick to score on the right. Beauxis then added a drop-goal to leave just two points separating the sides but then we had a try from replacement Gordon D'Arcy to leave the French needing two scores to win.
The first came from a Beauxis penalty with less than five minutes left but from the restart Cedric Heymans was pinged for holding on and Ireland secured a marvellous and fully deserved victory.
Ireland: R Kearney (G Murphy 76 min); T Bowe, B O'Driscoll, P Wallace (G D'Arcy), L Fitzgerald; R O'Gara, T O'Leary; M Horan, J Flannery (R Best), J Hayes, D O'Callaghan, P O'Connell, S Ferris, D Wallace, J Heaslip .
France: C Poitrenaud; J Malzieu, F Fritz, Y Jauzion, M Medard; L Beauxis, S Tillous-Borde; L Faure, D Szarzewski, B Lecouls, S Chabal, L Nallet capt, T Dusautoir, F Ouedraogo, I Harinordoquy.
Referee: N. Owens