In a historic occasion the two nations kicked off against each other in a World Cup match for the first time in forty years, with their last meeting coming at Spain 1982.
Early in the first half, France opened the scoring through a spectacular long shot from Aurelien Tchouameni in the 17th minute.
France winger Ousmane Dembele received the ball from Kylian Mbappe before laying it off deep to the Tchouameni who smashed long shot into the bottom left corner past Jordan Pickford.
A tight opening 45 minutes came to a close with France in the lead at 1-nil, with Tchouameni's long shot the only thing seperating the two sides.
The rest of the second half was a cagey affair with chances few and far between, England found themselves with several half chances in the first-half but none that were glaring misses.
Early in the second-half, Bukayo Saka won a penalty for England after dancing through the box before being brought down by an outstrecthed leg from Tchouameni.
Harry Kane stepped up to take the penalty and scored with aplomb, smashing it high into the top left corner and sending his club teammate Hugo Llloris the wrong way.
With his penalty, Kane became England's all-time joint top scorer alongside Wayne Rooney on 53 goals.
After conceding the equaliser, France quickly looked to put the pressure on England with several chances forcing Jordan Pickford into making a few good saves.
Just moments after Giroud came close to scoring with a side-footed volley, France took the lead in the 68th minute as the striker headed in from close range after getting on the end of a cross, redeeming himself and taking momentum back for France.
With just six minutes left of regular time, VAR awarded a penalty to England after Mason Mount was cynically barged to the ground by Theo Hernandez while looking to get on the end of a long ball.
The referee initially let play continue without awarding a foul, sparking upset and appeals from the England squad.
Harry Kane stepped up to take his second penalty of the match, giving the striker the opportunity to not only equalise but also score the goal that would make him England's all-time top goalscorer.
The England captain attempted to go for height but sent his penalty soaring well over the bar, with the miss leaving him looking distraught while the French players rushed around their keeper to celebrate.
In the closing minutes of the second half, England desperately continued their search for an equaliser but the French defence and in particular goalkeeper Hugo Lloris remained calm to maintain their lead.
As the full time whistle sounded, the French side erupted into celebration while the England players dropped to the ground in disappointment.
France will face Morocco in the semifinals after the African nation upset Portugal in their quarterfinal earlier this morning.
Jordan Henderson of England reacts after his teammate Harry Kane misses a chance to score a penalty kick during the FIFA World Cup Qatar 2022 Quarter-Final match between England and France. Photo: AFP / Salih Zeki Fazlioglu