Al Khor: Olivier Giroud scored the winner as defending World Cup champions France defeated England 2-1 on Saturday after Harry Kane missed a late penalty, setting up a semi-final against Morocco.
Aurelien Tchouameni drilled France ahead in the first half but Kane levelled from the spot after the break. Giroud's deflected header on 78 minutes sent France through as Kane then blazed over his second spot-kick of the match.
England were the better side for long stretches of the game at Al Bayt Stadium but, almost from nowhere, France went back in front when Giroud headed home with 11 minutes left.
Kane than blazed his second penalty of the game over the bar as England's wait to win a first major international trophy since the 1966 World Cup goes on.
France though remain on course to become the first side since Brazil 60 years ago to successfully defend the World Cup.
With Brazil having been eliminated on Friday and England dealt with here in the desert north of Doha, France are now surely the favourites to retain their crown as they prepare to face Morocco in the semi-finals.
This, remarkably, was the first meeting of these two great rivals in a major tournament knockout game, with Croatia's victory in extra time preventing England from joining France in the final four years ago.
England had found their stride after a sluggish start in the last-16 win over Senegal and it was no surprise to see Southgate name an unchanged side, with Bukayo Saka and Phil Foden either side of Kane in attack.
That meant he resisted any temptation to revert to a back five in an attempt to counter the threat posed by Kylian Mbappe, the tournament's top scorer with five goals.
There is no shortage of goal threats in the French side but few could have predicted that the opener would come from Tchouameni, the midfielder who is just 22 and had scored only once for his country before this game.
There was a touch of controversy to the goal, as it came from a France break which started with what looked like a foul by Dayot Upamecano on Saka.
Brazilian referee Wilton Sampaio waved play on, and Mbappe cut inside from the left before Ousmane Dembele and Griezmann combined to set up Tchouameni to hit a superb shot from 25 metres that curled away from Jordan Pickford and into the corner.
France had looked the more dangerous team before that, but England grew into the contest after falling behind.
Kane spun away from Upamecano in the box but was denied as his Tottenham teammate Hugo Lloris came out to dive at his feet.
Another moment of controversy followed as England thought they should have had a penalty when Kane was clearly fouled in a tangle of legs with Upamecano.
However, a VAR check ruled out a spot-kick with the officials judging that any infringement took place outside the box.
Not to be discouraged, Kane forced Lloris to tip a shot behind just before the half-hour mark and the France goalkeeper - winning a national record 143rd cap - was called into action again just after the restart to tip over a Jude Bellingham volley.
The pressure eventually told when Saka was brought down by Tchouameni in the area seven minutes into the second half and this time a spot-kick was given.
Kane stepped up to beat Lloris and score his 53rd goal to equal Wayne Rooney's record England tally.
The holders may not have been rattled, but England had the upper hand, and Harry Maguire headed agonisingly wide from a free-kick.
France had created nothing in the second half, but then Giroud forced an excellent save from Pickford following a Dembele knockdown, and moments later they struck.
Griezmann whipped in a tremendous cross from the left for Giroud to head in with the aid of a touch off Maguire.
That was not game over, as Theo Hernandez was penalised for a shove on substitute Mason Mount when the referee gave a spot-kick following a VAR review.
But this time Kane - with his country's outright goal record in sight - blazed over, and England's World Cup dream was over too.