In the 43 minute of the game, Les Blues were ahead as Djibril Sidibe scored on another rebound.
But a Kane penalty soon after the break - accompanied by a controversial decision involving the video assistant referee to send off Raphael Varane - allowed England to equalise, only for Dembele to finally take his chance and net the victor.
With France down to ten men England should have taken the initiative, but it was a sloppy ball from Gary Cahill which let Les Bleus in once again, allowing Ousmane Dembele to bag his first goal at global level, which turned out to be the victor.
The teams had come out to "Don't Look Back in Anger", the song by Manchester band Oasis which was played by the band and choir of the French Republican Guard, ably backed up by around 2,500 travelling English fans in one corner of the ground.
France eventually took the lead in the 78th minute as Mbappe turned provider to pick out Ousmane Dembele, who fired past Butland from the edge of the box.
That was highlighted on Tuesday, when England lost at France 3-2 despite playing most of the second half with an extra man against a team resting some key players.
Are players taking on Southgate's information?
"The best way to manage the game is to keep possession of the ball, make the opposition run, make sure we would be able to press because we've got a man extra".
"We just didn't manage that period of the game as well as we needed to, I thought we exhausted", said Southgate.
"I thought we looked more anxious while they went to 10 and they stepped up a level".
"Today is slightly different because I think we kept the ball as well if not better than France for long periods, but physically the demands that their players impose on you meant that we had problems with that".
In their last four competitive games, England have won only once - against minows Lithuiania - drawn once and have been beaten twice by Germany and France. Alli flicks on a long back and chases it himself, racing in behind the French defence at inside-left; Varane clips his heels, and the ref points to the spot! "We were down to 10 men, so hats off to the players, because that is a great England team", he told TF1.
'We will have to look back and see why.