Griezmann's second-half double, which came inside three crucial minutes, fired his side into the quarter-finals as they eventually showed their class at the Stade de Lyon.

However, for almost an hour, Ireland, who ended the game down to 10 men after central defender Shane Duffy was dismissed for a professional foul on the Atletico Madrid star, had threatened to gatecrash the party.

They took a second-minute lead through Robbie Brady's nerveless penalty after Paul Pogba's rash challenge on Shane Long, and France were booed off by a section of their own support at the break as they failed to rectify the damage.

But, as Martin O'Neill's men tired - they last played against Italy on Wednesday night, some three days after the French completed their group-stage matches - the hosts grew in strength and eventually ran out more comfortable winners than the scoreline suggests.

If Irish hearts has been broken by Swedish referee Martin Hansson's failure to spot Thierry Henry's handball at the Stade de France in November 2009, they were not to suffer again at the hands of Italian official Nicola Rizzoli.

The game was barely a minute old when Pogba barged Long to the ground inside the France penalty area, and Mr Rizzoli stunned the home crowd by pointing to the spot.

With Robbie Keane and Jonathan Walters sitting on the bench, it was Brady who stepped up to send Tottenham goalkeeper Hugo Lloris the wrong way and watch as the ball cannoned off the foot of the post into the net to send the massively outnumbered contingent from Ireland into ecstasy.

France's response came predictably swiftly as they pinned Ireland back deep inside their own half for long periods, although goalkeeper Darren Randolph enjoyed a largely uneventful first half.

He had to field a free-kick from West Ham team-mate Dimitri Payet which never threatened to over-extend him, and he was similarly untroubled by efforts from Griezmann and Pogba as the half wore on, although Lloris had to claw away a 21st-minute effort from Daryl Murphy - still awaiting his first senior goal for his country - while Duffy headed just wide.

With France dominating possession, aided by the industry of midfield general N'Golo Kante, O'Neill's men were having to defend deep and in numbers and, as the game became increasingly physical, Kante, Jeff Hendrick and Adil Rami all picked up bookings which meant they would miss the quarter-final should their side progress.

They very nearly got their reward in stoppage time when, after a flowing moved had left Pogba in space on the right, Payet accepted his pass and cut inside before seeing Stephen Ward block his shot with Duffy equally resilient from Griezmann's follow-up.

Having seen his players booed off by some members of the crowd at half-time, France boss Didier Deschamps withdrew enforcer Kante to send on the pacy Kingsley Coman, but it was central defender Laurent Koscielny who very nearly got theme back into the game when he glanced Payet's 48th-minute free-kick just wide.

Irish chances were few and far between, although Lloris did have to be alert to deny Long a 52nd-minute tap-in after James McClean had crossed from the left.

The pressure on their own goal was mounting by the minute, though, and, having seen Payet drag an effort wide, Randolph had to dive to his right to palm away Blaise Matuidi's well-struck 56th-minute shot.

But the French breakthrough was coming and, when it arrived, it did so in devastating style as the Republic's dreams were torn apart inside eight catastrophic minutes.

Payet picked out full-back Bacary Sagna on the right and his cross was inch-perfect for Griezmann to rise and head firmly past Randolph, to the immense relief of his countrymen.

However, his afternoon had only just started in earnest and just three minutes more had elapsed when he ran on to Olivier Giroud's expert knock-down and beat the keeper with an assured left-footed finish.

Griezmann was not finished as his 66th-minute run in behind the Irish defence prompted an ill-advised tackle by Duffy which earned him a red card and his increasingly beleaguered side any chance of a fightback.

Wednesday night's exertions took their toll on the 10 men as France attacked in waves throughout the closing stages, but the Republic did not suffer any further punishment as they battled all the way to the whistle.