Man-of-the-match Tommy Bowe ran in two first-half tries for Ireland but Declan Kidney's side's inability to put any points on the board after the break saw them pass up what was an excellent opportunity to beat France in Paris for only the second time in 40 years.
Ireland started brightly at a sodden Stade de France and were rewarded for their efforts on 13 minutes when Bowe intercepted Aurelien Rougerie's intended pass to Clement Poitrenaud before trotting in under the sticks for his 23rd international try.
Jonathan Sexton, who badly fluffed his first penalty attempt eight minutes into proceedings, added the extras and Ireland were in dreamland.
Scrum-half Morgan Parra got Les Bleus on the board just after the 20 minute mark after some incessant pressure from the French pack failed to yield the ultimate goal, a try.
Six minutes later an assured Sexton pushed the visitors seven points ahead again with a sweetly struck kick but Parra, kicking from just inside the half-way line, was quick to reply and with 30 minutes on the clock Ireland led 10-6 - game on.
Eight minutes later Bowe scored as good an Irish try as you're likely to see - the Ospreys star rose quickly from a challenge, lengthened his stride and lobbed a speculative chip towards the tryline before the bounce of the ball went his way and a dummy pass saw him evade the French defender before touching down. Sexton added the extras and at half-time Ireland led 17-6 and shock genuinely looked on the cards.
However, the second-half was all about France as Parra kicked two further penalties, thanks to Irish indiscipline and on 51 minutes Wesley Fofana went over for his third try in as many matches, following a loose kick from the otherwise impeccable Rob Kearney.
Parra's conversion attempt slid just wide of the right-hand post but the Clermont Auvergne number nine levelled things up just seven minutes later and that's how it stayed as the first draw between the sides since 1985, in what was then the Five Nations, and is now the Six Nations, came to pass.