Ireland must chase World Cup glory without talismanic captain Paul O’Connell, and potentially Johnny Sexton, Sean O’Brien and Peter O’Mahony, as their seismic 24-9 victory over France comes at a huge cost.

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O’Connell’s Test career looks over after 108 caps, the Toulon-bound lock punching the turf in agony with a serious leg injury as Ireland set up a quarter-final with Argentina.

Linchpin fly-half Sexton trudged out with a groin strain and nursing sore ribs from a hefty hit from Louis Picamoles, while Sean O’Brien could face a citing for an alleged punch on Pascal Pape.

Combative flanker O’Mahony departed via a stretcher with a suspected knee problem amid the second-half maelstrom, as the toll of a searing contest grew and grew.

Ireland will now meet the Pumas in the last eight, avoiding defending-champions New Zealand and lining up their best-ever crack at a first World Cup semi-final.

Totemic lock O’Connell will retire from Test rugby at the end of Ireland’s World Cup campaign, but will surely now miss the rest of the tournament.

Rob Kearney and Conor Murray claimed the tries to subdue a stunned France, whose pre-match fighting talk evaporated under real pressure.

Madigan stepped out of Sexton’s shadow in fine style too, bossing Ireland’s line with poise and authority, while O’Brien and Robbie Henshaw turned in performances critical to this win.

Ireland’s retribution for Pape’s cheap-shot knee to Jamie Heaslip in the Six Nations was for O’Brien to smash the Stade Francais lock square in the ribs.

Irrespective of whether the citing commissioners review the incident, O’Brien set Ireland’s tone, with Pape prone on the turf for several minutes.

France rejected a shot at goal in favour of kicking to the corner, only for Ireland to force a choke-tackle turnover. Frederic Michalak fluffed his first effort from the tee, before chipping his second against the post.

Scott Spedding and Sexton traded penalties for six points apiece, before Ireland’s backline general was forced out of action.

France spent all week threatening to take Sexton out of the game, and the former Racing Metro playmaker lasted just 24 minutes.

Number eight Picamoles’ thundering hit left Sexton prostrate on the field, before he trudged off disconsolately, hiding his face with his shirt.

Sexton’s departure threw Madigan to the wolves, but the Leinster fly-half fired a penalty to calm any nerves and edge Ireland 9-6 ahead.

Ireland shredded the French line with Tommy Bowe searing clear before seeming to fire the scoring pass to Keith Earls.

Somehow Earls lost the ball amid a full-tilt juggling act however, letting France hugely off the hook.

Robbie Henshaw pulled off a desperate turnover penalty just yards from his line to stave off the attack, but in the build-up talisman O’Connell suffered either knee ligament damage or a torn hamstring.

Ireland refused to relent on their stunning intensity after the turnaround, Iain Henderson replacing O’Connell and centre Henshaw maintaining his pivotal performance.

France knocked on in a try-line scramble, and from the scrum Rob Kearney powered home for the game’s first try.

Morgan Parra nudged a penalty to reduced Ireland’s lead to just five points just past the hour-mark, teeing up a nervy final quarter.

Rory Best powered close, then Murray nipped home – cleverly placing the ball against the post to claim the try.

Madigan’s conversion put Ireland 21-9 to the good, before the Leinster playmaker posted a penalty to seal the deal.