The closing moments were spent worrying over Ireland's substitute scrum-half Eoin Reddan, who was administered oxygen and then carried off after suffering a broken leg.
Reddan has been ruled out for three months after falling awkwardly beneath a tackle in the final minute.
The match was viewed as one both sides needed to win to revive their dismal championships.
It produced a draw, even though Ireland led 13-3 at half-time having delivered a tactical masterclass in treacherous conditions.
It was the second successive draw between the rivals after last year's showdown in Paris finished 17-17.
But Head coach Declan Kidney refused to complain about Ireland's injury-depleted ranks.
"We took a conscious decision that we wouldn't complain about things. Other people are worse off than we are, plus it's such an insult to the lads coming on and having a huge go," Kidney said.
"On any given day Paul O'Connell, Tommy Bowe, Stephen Ferris and Jonathan Sexton would be in the running for a Lions spot.
"I've never experienced an injury run like this, but you work your way through and I spoke to (captain) Jamie Heaslip about it and we agreed not to complain."
We're frustrated, but there are lads coming in who have no experience at this level under their belts and are doing such a good job for us.
Declan Kidney
Ulster fly-half Paddy Jackson responded courageously to his painful debut against Scotland by landing two enormous penalties and converting Heaslip's 11th-minute try.
Jackson's debut at Murrayfield two weeks ago was ruined by a performance from the kicking tee that contributed to the 12-8 defeat - but the 21-year-old impressed on Saturday.
In similar weather against England four weeks ago, the Irish tactics were ill-judged - but they played with far greater intelligence in their penultimate match of the championship.
The final quarter witnessed a reversal of fortunes, however, and they paid the price for failing to capitalise on a dominant spell shortly after half-time.
As the match neared its conclusion, winless France began to kick with greater accuracy, used the driving maul and were given impetus by their substitutions to stage a comeback in the final moments.
Disaster struck for Ireland when Picamoles barged over with seven minutes remaining and Michalak landed the challenging conversion to level the score.
Picamoles and Vincent Debaty then intervened to deny Earls a possible try as the match headed for a nerve-shredding climax.
The players are down, but that's the measure of how much they push themselves and why I stand by them so much.
Declan Kidney
"The players have taken everything that's been thrown at them and just got on with it," Kidney said.
"So to put our foot forward like that and be creating in the way we are doing actually adds to the frustration."
"In another time the team would be so much stronger for what's happening at the moment."
Captain Heaslip also voiced his frustration at the late French comeback.
"The feeling is that was a match we could have won has been there for the last three games," Heaslip said.
"A draw is always a strange one. That game in particular we could have won. It's a bit weird and the changing room is flat.
"There were a lot of positives in the game, but we gave them easy outs at important moments and you shouldn't give France that opportunity. It's a hard one to take."
The draw may mark the end of former captain Brian O'Driscoll's international career on home soil.
The star was given a huge ovation by the crowd at the Aviva Stadium.
Injured lock Donnacha Ryan and centre Luke Marshall are doubts to face Italy next Saturday, while flanker Peter O'Mahony, scrum-half Conor Murray, centre O'Driscoll and wing Fergus McFadden also picked up a variety of knocks.
Already missing for Ireland were lock Paul O'Connell, wings Tommy Bowe and Craig Gilroy, centre Gordon D'Arcy, flanker Stephen Ferris and fly-half Jonathan Sexton.