A try from powerful France number eight Louis Picamoles salvaged a 13-13 result against Ireland as they left the Aviva Stadium with a point.
The Toulouse man's try six minutes from time, converted by Frederic Michalak, ensured the French ended their run of three straight defeats.
It had looked like Ireland would hold on to pick up a priceless Six Nations win but a series of injury concerns over Brian O'Driscoll and Luke Marshall left the hosts scrambling for fit players before Picamoles crashed over in the 73rd minute.
It was the second successive draw between the two sides but extended France's winless streak over the past two Six Nations to seven, their worst run since 1926-27, and leaves them needing to beat Scotland at home next Saturday to have any chance of avoiding the wooden spoon.
The Irish made the early running in terrible weather conditions and were rewarded after a superb tactical kick deep into the French 22 by O'Driscoll set up a lineout.
Peter O'Mahony won the ball and from the resulting driving maul Heaslip squeezed over the line to score his eighth international try — Jackson belied concerns over his place-kicking, after a disastrous performance against Scotland, by landing a superb conversion.
France were presented with a golden opportunity to reduce the deficit in the 16th minute but Michalak, whose selection had raised eyebrows after three poor performances, missed his penalty from close range.
Ireland were very much in control but Jackson missed a chance to make it 10-0 in the 23rd minute as his penalty from long range drifted wide.
Michalak made no mistake with his second chance in the 27th minute as he slotted over a penalty to make it 7-3.
However, the Irish scrum were forcing the French into infringement after infringement and Jackson, assuming responsibility when the Irish could have kicked for the corner, opted for a kick at goal from long range in the 30th minute and converted it to restore the seven point advantage.
The 21-year-old, playing in only his second test, was showing little fear and he punished the French again three minutes later as he stroked a penalty over from about 45 metres for 13-3 which even had injured first choice fly-half Jonathan Sexton grinning and applauding from the stands.
Michalak's woeful first-half finished on a suitably low note as given the chance to give France a filip on the stroke of half-time he sent another kickable penalty wide to leave the Irish sitting comfortably enough at the break.
Jackson had an early chance in the second-half to extend the lead but his effort fell just short.
The Irish were still controlling the game but prop Mike Ross conceded a penalty in the 54th minute and Morgan Parra stepped up, replacing the misfiring Michalak, and converted it for 13-6.
Parra, though, proved he too was fallible, missing a tough penalty attempt just before the hour mark as the French started to pressure the hosts into a series of errors.
The visitors pressed forward desperate to redress the balance but saw a chance go begging as with extra men wide out to the right they failed to push home the advantage and the Irish defence held firm.
However, eventually the French breached the line as Picamoles took advantage of Ireland dithering after a penalty was awarded and tapping it quickly he touched it down for his fifth try for his country — Michalak stepped up to the task and converted for 13-13.
The scorers:
For Ireland:
Try: Heaslip
Con: Jackson
Pen: Jackson 2
For France:
Try: Picamoles
Con: Michalak
Pen: Michalak, Parra
Ireland: 15 Rob Kearney, 14 Fergus McFadden, 13 Brian O'Driscoll, 12 Luke Marshall, 11 Keith Earls, 10 Paddy Jackson, 9 Conor Murray, 8 Jamie Heaslip (c) 7 Sean O'Brien, 6 Peter O'Mahony, 5 Donnacha Ryan, 4 Mike McCarthy, 3 Mike Ross, 2 Rory Best, 1 Cian Healy.
Replacements: 16 Sean Cronin, 17 David Kilcoyne, 18 Stephen Archer, 19 Donnacha O'Callaghan, 20 Iain Henderson, 21 Eoin Reddan, 22 Ian Madigan, 23 Luke Fitzgerald.
France: 15 Yoann Huget, 14 Vincent Clerc, 13 Florian Fritz, 12 Wesley Fofana, 11 Maxime Medard, 10 Frederic Michalak, 9 Morgan Parra, 8 Louis Picamoles, 7 Thierry Dusautoir, 6 Yannick Nyanga, 5 Yoann Maestri, 4 Christophe Samson, 3 Nicolas Mas, 2 Benjamin Kayser, 1 Thomas Domingo.
Replacements: 16 Guilhem Guirado, 17 Vincent Debaty, 18 Luc Ducalcon, 19 Sebastien Vahaamahina, 20 Antonie Claassen, 21 Maxime Machenaud, 22 Francois Trinh-Duc, 23 Mathieu Bastareaud.
Referee: Steve Walsh (Australia)
Assistant referees: Wayne Barnes (England), Greg Garner (England)
Television match official: Nigel Whitehouse (Wales)
A match dominated more by the whistle and boot than any real memorable moments of attacking flair, Scotland and Wales racked up a total of 28 penalties between them as both sides continued to displease referee Craig Joubert.
It's the first time since 2001 that the Scots have won back-to-back Six Nations matches.
France were transformed from the sluggish side that were abysmal against Wales a fortnight ago — aggressive at the breakdown and benefiting from moving Wesley Fofana back into the centre after his ill-fated stint on the wing.
A severe downpour before kick-off hindered the handling ability of both sides through the first half, with Leigh Halfpenny adding three penalties for the visitors and Kristopher Burton responding with two for the hosts.
Stuart Lancaster's outfit put in another mature effort that leaves them as the last remaining unbeaten side in the 2013 Championship.
A solitary late try from wing George North handed Wales the spoils in a dour game that culminated to the sound of boos and whistles from the Parisian crowd.
Four tries, including a brilliant length of the field interception try from Stuart Hogg, led to a memorable victory for Scotland in front of a vocal home crowd at Murrayfield, compensating for the performance against England at Twickenham last weekend.
It was a sensational victory for the Azzurri who have now managed to beat Les Bleus twice in the last two years following their famous win in 2011.
The hosts enjoyed large portions of possession in both halves and arguably should have come away with more points, despite racking up four tries through Chris Ashton, debutant Billy Twelvetrees, Geoff Parling and Danny Care.
A dire performance from Wales in the opening 40 minutes left them with a mountain to climb in the second-half, at which they threw everything to bounce back from a 30-3 scoreline to 30-22 in an utterly dominant half.
The loss meant that Wales, the current Grand Slam champions and World Cup semi-finalists, fell out of the top-eight seeds for RWC 2015, the draw for which takes place on Monday.
New Zealand responded to a 15-0 defecit with scores from Julian Savea and Kieran Read, before England took charge thanks to three of their own from Brad Barritt, Chris Ashton and Manu Tuilagi in an astonishing second-half performance.
The visitors crossed the whitewash on five occasions with Wyles bagging a brace, while Andrew Suniula, Paul Emerick and Takudzwa Ngwenya also added their name to the scoresheet.
Three penalties from Pat Lambie and a bizarre try from Willem Alberts handed the visitors the win, with Toby Flood and Owen Farrell accumulating five penalties between them.
Ireland led from start to finish in a dominant display, outscoring their visitors seven tries to two.
Unlike their convincing successes over Australia and Argentina this month, victory didn't come easily for the French, who were trailing the Islanders going into the final quarter.
Predictions the All Blacks' attack would incinerate Wales' defence came to fruition in the first half especially. However even though the scoreline may read otherwise, it was a much better effort from the Welsh - the second half especially.
Scotland led 6-3 at half-time but second-period tries from Tukulua Lokotui and Fetu Vainikolo saw the Pacific Islanders earn their first ever Test triumph on the European stage