Ireland had an excellent start with Robbie Brady scoring a second minute penalty, and it was an even affair for both sides throughout the rest of the first period, with Griezmann, Daryl Murphy and Paul Pogba all having goood chances, but none could stop Ireland leading at the break by a single goal.
France turned up the heat in the second period with good opportunities for Laurent Koscielny and Blaise Matuidi before Griezmann equalised just before the hour mark, before adding the second minutes later. Shane Duffy was then dismissed for the Irish before Andre-Pierre Gignac rattled the crossbar, but the French had done enough to progress.
There was only a small Irish constituency inside the Stade des Lumières, and couldn't haven't wished for a better start as they won a penalty inside the first minute. Shane Long was about to pull the rigger before being bundled over by Pogba, and Nicola Rizzoli had no hesitation in pointing to the spot, Brady followed up his winner against Italy as he sent Hugo Lloris the wrong way, as his set piece clattered the post as it went in.
Didier Deschamps' side looked to get back in the game, and almost did when Pogba produced an excellent cross for Griezmann but the striker should have done better with his effort, as the header went over the crossbar.
Martin O'Neill's side almost added a second in the 21st minute, Murphy managed to produce an excellent volley, and looked to have done everything right, but Lloris did well to push the effort away from goal.
Pogba had produced an electric performance in the goalless draw with Switzerland, and looked to top that as he tried his luck with a dead ball situation from 30 yards, but Mark Randolph did well to take the sting out of the midfielder's effort, before collecting at the second time of asking.
The Irish produced some heroic defending to keep their lead, as the half entered it's final moments. Oliver Giroud did well to tee up Dimtri Payet, who managed to get away from two defenders before pulling the trigger, but Stephen Ward dived in with the block and the Irish did even better to block the second attempt from Griezmann.
Griezmann changes the game
Deschamps' side came flying out of traps as the second half began, a free-kick in from Payet took the slightest deflection off Ward, which seemed to distract Koscielny as he glanced his header at the far post wide. Matuidi followed that up as he tried one from distance but Randolph again managed to produce a decent save.
France had been knocking on the door for sometime, and managed to break through just before the hour mark. Payet produced an excellent cross which found Griezmann, and the little striker did excellently to get up and produce a powerful header which Randolph could only help into the net.
The Atletico Madrid striker turned the game on it's head, as he added his, and France's second, to give them the lead, just two minutes after equalising. A long punt upfield was excellently headed down by Giroud, into the feet of Griezmann and he coolly slotted into the bottom corner, to send the French fans into hysteria.
It got worse for the Irish as they were reduced to ten men, Giroud put Griezmann through once again, and looked to be through for his hat-trick, but Duffy took one for the team bringing the striker outside the area and was rightly given his marching orders.
Substitute Gignac managed to cut inside before curling an effort towards goal, but his effort clattered the crossbar.
The final opportunity came five minutes from the end, as Gignac looked to add a third and almost did, when he got on the end of a ball into the area, but his effort glanced past the far post.