Olivier Giroud scored in the 78th minute at Al Bayt Stadium to keep France on course to become the first team since Brazil in 1962 to win back-to-back World Cups.
Giroud raced away in delight when his header deflected off England defender Harry Maguire and sailed past goalkeeper Jordan Pickford.
England striker Harry Kane had a chance to even the score late in the match but he sent a penalty attempt over the bar.
It was his second spot kick of the match. He earlier scored to make it 1-1 after Aurelien Tchouameni had given France the lead in the 17th minute with a powerful drive from 20 meters (yards).
France will next face Morocco in the semifinals on Wednesday. The Moroccans became the first African team to reach the semifinals at the World Cup by beating Portugal 1-0.
England had been looking like the team more likely to score when the match was at 1-1. But instead it was Giroud who connected with Antoine Griezmann’s cross to extend his record as France’s all-time leading scorer to 53 goals.
The celebrations didn’t last long, however, as referee Wilton Sampaio reviewed a challenge from Theo Hernandez on substitute Mason Mount in the box. The Brazilian official awarded the penalty.
Kane sent Tottenham teammate Hugo Lloris the wrong way with his earlier penalty kick after Tchoumani brought down Bukayo Saka, but he lifted his next effort high over the bar.
England, which lost to Italy on penalties in the final of last year’s European Championship, reached the semifinals at the 2018 World Cup.
After scoring 12 goals on the way to the quarterfinals in Qatar, England trailed in the match for the first time at the World Cup. It was also the first time the English team had conceded a goal since the opening 6-2 rout of Iran.
Kane’s goal was his 53rd for England, moving him into a tie with Wayne Rooney for the most goals scored for the national team.
Mbappe didn’t have have a goal of his own to celebrate, but cheered passionately after Kane’s penalty miss. Mbappe is the leading scorer at the World Cup with five goals, one more that Giroud and Lionel Messi.
England coach Gareth Southgate has often been criticized for being too cautious in the biggest games, but he opted for a back four against France and loaded his team with attacking threats.
Maguire kicked the ball out of play at the very beginning of the match even though there was no pressure from a France opponent. Air was leaking out of the ball and Maguire informed the referee that a new one was needed.