But France were rewarded for their impressive response to the setback when Dembele lashed a finish across the goal and into the net 12 minutes from time.
Before the game, a touching tribute to the victims of the Manchester and London terror attacks saw a rendition of "Don't Look Back In Anger" and a minute's silence.
England will be disappointed with the manner in which they lost the game, though it was something of an experimental side named by Gareth Southgate, who handed a first cap to Tottenham full back Kieran Trippier.
Stones endured a disappointing night at the heart of England's defence and was given just three out of ten by L'Equipe, who are renowned for their ruthless ratings.
On the penalty: "I've not seen it again, but from my initial view I thought it was the right call". They stood side by side as a moving tribute to the victims of the Manchester and London attacks took place.
The 23-year-old has undoubted talent but had a hard first campaign at Etihad Stadium and his performance must be placed in the context of a lack of game time after suffering a muscular injury towards the end of last season.
"The pleasing thing is that the players are taking on board tactical information".
After a friendly against Spain in March in which France had a goal disallowed and saw a Spain goal given in a 2-0 loss at Stade de France, replay struck again.
It was not enough, however, to deny a spirited and daring French side. But I think we've had to play at our absolute limit to stay in all three of the matches, which has shown in the latter stages of those games.
The 23-year-old's extraordinary form has had some England fans thinking it's all a bit too good to be true.
After the break, Tottenham talisman Kane equalised from the spot after Raphael Varane was sent off for a challenge on Dele Alli.
"It was a bit tricky with the penalty and the red card".
France coach Didier Deschamps had doubts about the referee's decision. Some 2,321 England supporters had tickets to the game.
England's numerical advantage showed immediately after the equaliser, as they dominated possession, but France built back into the game and were clearly intent on playing for the win despite the absence of Varane.
· Kane has now scored 11 times in his last five appearances for club and country.