Six Nations holders France clinched victory in Dublin despite scoring only one try to Ireland's three.
The Irish paid heavily for indiscipline as five penalties by Morgan Parra and one by his replacement Dimitri Yachvili proved to be the difference.
A first Test try by Fergus McFadden and a Tomas O'Leary touchdown helped Ireland to a 15-12 half-time lead.
Winger Maxime Medard raced through for the French try with Jamie Heaslip's score setting up an exciting finish.
The Irish staged a late rally but it came to nothing and Declan Kidney's men were left to reflect on their error count. Overall, they conceded 16 penalties with nine awarded against the French.
Ireland, knowing they needed an improved performance after sneaking a narrow win away to Italy, had made a confident start.
Full-back Luke Fitzgerald thought he had got in for a try in the left corner in the third minute but Gordon D'Arcy's pass to him had been forward.
However, the try was not long in coming as Leinster wing McFadden scored in his second Test.
Clement Poitrenaud was guilty of dropping the ball in his own 22, McFadden pounced on it and reappeared a few phases later to pick up and charge over from close range, with Sexton converting for 7-0.
France got their first point in the 12th minute through a Parra penalty after David Wallace failed to release a tackled player.
Sexton, though, restored Ireland's seven-point advantage after the French scrum collapsed.
However, Irish indiscipline in not rolling away enabled Parra to land three successful penalties which edged the visitors into a 12-10 lead.
Rougerie break sets up Medard try
Ireland got their second try not long before half-time with O'Leary, an injury doubt all week with a stiff back, just about getting over for a try which was confirmed by the video referee.
Sexton sliced his conversion attempt so the Irish went in at half-time with a fragile-looking three-point advantage.
Parra maintained his 100% kicking record with a fifth penalty to bring the sides level before Medard scored France's only try in the 55th minute.
Aurelien Rougerie charged straight at D'Arcy, and when the Leinster centre missed the tackle, was able to offload the scoring pass to Medard.
The game seemed to be up for Kidney's men in green as the momentum was certainly with France.
But Ireland dug out a gutsy response and applied pressure which resulted in number eight Heaslip diving over in the corner to revive home hopes.
Replacement fly-half Ronan O'Gara added the two points with a touchline conversion which went in off the far upright, but France held on.
France will now travel to face England, the other unbeaten side in the tournament, at Twickenham on Saturday, 26 February, in a pivotal match that could decide the likely destination of the title.
Ireland will head to Murrayfield to face winless Scotland in a fortnight.
Ireland: Fitzgerald; McFadden, B O'Driscoll, D'Arcy, Earls; Sexton, O'Leary; Healy, Best, Ross, O'Callaghan, O'Connell, O'Brien, D Wallace, Heaslip. Replacements: O'Gara for Sexton (63), Reddan for O'Leary (70), Court for Healy (56), Cronin for Best (76), Cullen for O'Connell (80). Not Used: Leamy, P Wallace.
France: Poitrenaud; Huget, Rougerie, Traille, Medard; Trinh-Duc, Parra; Domingo, Servat, Mas, Pierre, Nallet, Dusautoir, Bonnaire, Harinordoquy. Replacements: Clerc for Poitrenaud (51), Jauzion for Traille (73), Yachvili for Parra (54), Marconnet for Domingo (50), Thion for Pierre (64), Chabal for Bonnaire (54). Not Used: Guirado.
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