Halfback Conor Murray's try with eight minutes remaining sealed the victory for Ireland, who despite having a wealth of possession and territory, couldn't quite put France away for good until then.
Their quarter-final opponents will be an impressive-looking Argentina in Cardiff on Monday morning and much will depend on their injury reports after this brutal match.
A day before that the All Blacks will take on France. The French, well, who knows how they are travelling? As we have seen so often in World Cups, their pool form counts for nothing, especially against the All Blacks.
However, Steve Hansen's men have it all in their favour. They have had an extra 48 hours to prepare for their date with destiny after their good win over Tonga and will be confident they have the muscle and firepower to sink their grand final opponents from the last, for them, glorious, World Cup.
The Irish, playing in front of a crowd of 72,000, most of whom seemed to be dressed in green, thoroughly deserved their victory. New Zealand-born coach Joe Schmidt has turned them into a tough and combative outfit who are extremely well organised on defence.
Their attack stuttered in the first half, with centre Keith Earls bombing a try when dropping a pass with the line open after 30 minutes, but impressive fullback Rob Kearney gave them the upper hand after the break with a try and Murray made it safe with one of his own against the right-hand post.
Flanker Sean O'Brien dominated at the breakdown - not even French skipper Thierry Dusautoir could rally his men there.
Ian Madigan, the impressive replacement for Sexton, added a penalty to put some gloss on the scoreboard as the Irish finished well on top for a win every bit as brave as Australia's over Wales at Twickenham in their final pool match.
In the end the match was played out to the strains of Fields of Athenry and this really did seem like a home match for Ireland. Will they miss O'Connor, O'Mahony et al against a tough Pumas team? Possibly, but their supporters will enjoy this victory - their first World Cup win over France in four times of trying - for a long while.
Ireland 24 (Rob Kearney, Conor Murray tries; Jonny Sexton 2 pens, Ian Madigan 2 pens, con)
France 9 (Scott Spedding 2 pens, Morgan Parra pen)
Halftime: 9-6
By Patrick McKendry at the Millennium Stadium
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