Ireland had only won twice in France in the past 40 years, and not at Stade de France since 2000, but a victory looked there for the taking after winger Tommy Bowe's two tries put the Irish 17-6 up at halftime.
"We were struggling at halftime. The players showed great spirit to come back, but when you give 10 points away to Ireland it becomes hard to win the game," France coach Philippe Saint-Andre said.
"We wanted to start well in the first 15 minutes, but we played a bit too much in our half. It was when started to take control of the match that we conceded a (second try)."
France failed to show much attacking creativity, and profited from an Ireland lapse in midfield to get back into the game when centre Wesley Fofana scored his third try in consecutive games early in the second half.
France needed the steady kicking of scrumhalf Morgan Parra, who landed all four of his penalties, to escape with a point.
"We're very disappointed with the result, although we came back into it well," France captain Thierry Dusautoir said.
"In the dressing room it felt like a defeat," Saint-Andre said. "The Irish defend very well and contest the breakdown well. You have to congratulate the Irish, but you can't give points away easily like we did."
Wales can clinch the Grand Slam by beating Italy and then France at home. France won its opening two matches, at home to Italy and away to Scotland, and plays England at Stade de France next Sunday.
Bowe was at his opportunistic best, reading France centre Aurelien Rougerie's telegraphed pass to intercept and score his first try. He scored his second from a brilliant individual effort, leaving the French defence stranded in a 60m run.
Ireland coach Declan Kidney said his team gave away too many sloppy turnovers in the second half.
"If you're not disappointed after you don't win, you shouldn't be in the job," Kidney said.
Ireland captain Paul O'Connell echoed that sentiment.
"We're really disappointed with our second half performance," he said. "We're very frustrated."
Ireland started the tournament with a last-minute home loss to Wales, before thumping Italy 42-10 last weekend.
"We had an outstanding first half. We put them under so much pressure but to come away with no points in the second half is a huge disappointment, and it's a very quiet dressing room," Bowe said. "Obviously we were very happy with the first half, to score two tries over here is very difficult."
As in the previous two matches, France flyhalf Francois Trinh-Duc struggled with his tactical kicking game and Ireland quickly started to get on top.
Ireland took the lead when France decided to run the ball from its 22-yard line and Rougerie's casual pass popped up invitingly for Bowe to run unchallenged and touch down under the posts in the 13th minute. Ireland then gave away a penalty for offside and Parra slotted over from close range to make it 7-3.
But France was struggling to withstand Ireland's power in the scrum and gave away another penalty, which Jonathan Sexton converted for 10-3.
"We made too many mistakes in the ruck early on," Dusautoir said.
The French pack finally forced Ireland to retreat as the half wore on, and referee Dave Pearson awarded another penalty. Parra kept France within touching distance with a fine kick from 45m.
Ireland regained control shortly before the interval.
The ball was spun along the line from left to right, and Bowe was 60m out when he collected a pass, palmed off a weak tackle from Fofana, kicked the ball expertly over the head of fullback Clement Poitrenaud, judged the bounce perfectly and sprinted into the right corner. Sexton's conversion hit the inside of the post and sneaked over to put Ireland firmly in command.
France started the second half brightly and Parra whipped the ball out to the blindside to Rougerie but Poitrenaud fumbled his pass.
Thankfully for France, Parra kicked over a crucial penalty from a difficult angle wide left to make it 17-9.
Fofana then scored a fine solo try. Trinh-Duc picked up a loose ball in midfield and quickly fed Fofana, who set off on an angled run and brushed off fullback Rob Kearney's desperate tackle to slide over near the corner.
Parra tied the match with another clinical penalty from 40m.
Ireland scrumhalf Connor Murray hurt his right knee after landing awkwardly and was replaced midway through the second half by Eoin Reddan.
"Connor probably hyper-extended his knee," Kidney said. "It doesn't appear the ligaments are damaged."
After Lionel Beauxis had missed with two drop goal attempts, left winger Julien Malzieu galloped down the wing but was held up just short of the line.
