Having been labelled Six Nations favourites by England coach Eddie Jones, Ireland had controlled the game in the first half thanks to Johnny Sexton’s experienced boot both out of hand and from the tee.
But they could not find a five-pointer and in truth created precious few opportunities to do so.
The gap remained just six when they were caught by Teddy Thomas’ sucker-punch with less than 10 minutes left, and could not find an extra gear in which they might have scored a try.
However, Sexton had one more crack at the game when Ireland edged into the French half and with the clock red, the fly-half knocked the most dramatic of drop-goals to end the match.
“It was one of those moments. I was just happy I got another chance,” said Sexton, who had missed a penalty to give Ireland a nine-point lead.
After the frenetic nature of the opening match of the tournament, the first 10 minutes were veritably cagey.
The two men controlling each attack could hardly have been more different, with fly-half Sexton earning his 68th cap and his opposite number winning his very first.
Matthieu Jalibert at 19 is France’s youngest ever No 10 but his debut, just his 16th game of professional rugby, last only 29 minutes before a knee injury curtailed his afternoon.
In a team so often paralysed by an impatient Parisian home crowd, Jailbert was one of the few to play with some freedom but little came off as Ireland’s experienced defence left him little to play with.
And by the time he departed, Sexton had metronomically given the visitors a narrow but deserved six-point lead.
He added another before the break while scrum-half Maxime Machenaud ensured the deficit remained one score and while Ireland never ran away with the game, the second half saw the Irish exploit their experience.
While Sexton played territory and ground out the game, the French disintegrated into familiar ill-discipline.
Time and again, the pack found themselves penalised by Nigel Owens at the breakdown with Sebastien Vahaamahina particularly drawing the referee’s eye on multiple occasions when France had good field position.
And then, out of nowhere, the first try of the match went France’s way. Ireland were made to pay for failing to turn territory and possession into more points when Thomas broke down the right, through Conor Murray, and turned on his speed, jinking past Jacob Stockdale to score from 60 metres out.
However, Ireland had the last laugh when Sexton somehow smashed a drop-goal from 45 metres to seal a remarkable win.