Just before the break, Les Bleus took the lead, with Monaco full-back Djibril Sidibe firing home after superb work from Dembele.
Kane made it 2-2 for England from the penalty spot straight after the restart after Varane had felled Dele Alli, a foul for which he was shown a red card after the intervention of assistant referee Marco Guido.
Raphael Varane was sent off before a penalty was sacked home by Kane, with Les Bleus rallying as Ousmane Dembele capped a fine display by wrapping up a 3-2 victory that left Southgate frustrated.
However, on 78 minutes, Dembele would get France's third goal of the game, after being set up by Mbappe following some dismal England defending.
There were several expected changes made by Three Lions manager Gareth Southgate, but Kane refused to use the differing personnel as an excuse.
But it did England no good and 12 minutes from time the French got the goal they deserved, Mbappe teeing up Dembele for the decisive score of the evening.
"I think with the ball generally we are progressing", he continued. We just weren't good enough, " Kane said on ITV.
"But clearly even with video not every decision will be 100 (per cent) - you won't get every single decision right".
"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".
"There'll still be an element of one person's judgement within that".
Tuesday's match was never going to be as embarrassing as their last clash on French soil, given the Three Lions bowed out of Euro 2016 to Iceland at the last-16 stage in Nice.
Olivier Giroud had an effort ruled out for offside and France were forced into an early change - the first of many substitutions - as Lucas Digne replaced the injured Benjamin Mendy.
England face a different test when they return to action in September, with the World Cup qualifier in Malta, ranked 182nd in the world, followed by Slovakia, the side second in Group F, coming to Wembley.
"We have been competitive in all three games but we needed to play at our absolute limits to stay in all of those matches and that has shown in the end". He tries to move the ball outside, Bertrand puts is back into his stride, and he speeds into the box, feints outside, ducks inside as Stones goes shopping, and shoots low and hard.
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