The striker had drawn his side level in the Al Bayt Stadium with a successful spot kick that saw him match Wayne Rooney's record haul of 53 goals for England.
He then had the chance to make it 2-2 late on after Mason Mount was barged over by Theo Hernandez in the area but this time he blazed his effort high over the crossbar.
After the final whistle, Kane dropped to his haunches and stared at the ground before walking tearfully away to be comforted by England manager Gareth Southgate.
"I'm not someone who thinks too much about it, I prepare the same whether I get one penalty or two penalties in a game," Kane told the BBC about facing his Tottenham Hotspur team mate Hugo Lloris from the spot for the second time.
"I can't fault my preparation or the detail before the game, it didn't feel any different. I felt confident taking it but didn't execute it the way I wanted to.
"Of course it's something I will have to live with and take on the chin. But all we can do is be proud of each other and know that the team is in a really good place for the future."
Kane's miss will be added to some infamous England penalty failures at major tournaments with the likes of Southgate, Chris Waddle and Stuart Pearce all haunted by them, although theirs all happened in penalty shoot-outs rather than in regular play.
"As you'd expect he's very, very low, but he has nothing to reproach himself for," Southgate said of Kane. "We're in a position we are as a team because of his leadership and goals."
Kane's converted spot kick in the second half was his fourth successful conversion at World Cups, not including shoot-outs - more than any other player in World Cup history.
SOUTHGATE'S FUTURE
Southgate cut a disconsolate figure at the end of the game, but said he would not make any decision about his future in the heat of the moment.
"Whenever I finish these tournaments, you need time to make the correct decision. Emotionally, you're going through many different feelings," Southgate told reporters.
"The energy that it takes in these tournaments is enormous. I want to take the right decision, whatever that is, for the team.
"In the past my feelings have fluctuated in the immediate aftermath of tournaments."
However, Southgate said he was still proud of his squad after they went "toe-to-toe" with the reigning champions.
"They know how close they've come, they know they pushed a top nation all the way, they had more possession, more attempts on goal, I'm very proud of how they've been - not only tonight but whole tournament," he said.
"Young players have announced themselves on the world stage, we showed a different side of ourselves in the way we played, we showed character to come back from going behind tonight.
"We've had consistent performances over three tournaments. Tonight is the best we've played against a major nation since I've been in charge, but we have fallen short. In the end, the scoreline is what matters."
England's players were incensed in several moments during the game when the referee's decisions did not go their way but Southgate chose not to wade into any controversy.
"We've lost a game, I don't think we should be speaking about referees," he said.
"I can just compliment France and wish them good luck. They're a fantastic team. They've got some brilliant players and Didier (Deschamps) has done a fantastic job. So congratulations to them."
France's 2-1 victory means they will play Morocco in the semi-finals.
