England captain Kane put them ahead from close range from a low Ryan Bertrand cross before the 10-minute mark.
Even after Raphael Varane was sent off for clumsily felling Dele Alli - Kane dispatched the 48th-minute penalty - France continued to attack with gusto and, after Mbappe rattled the crossbar, Borussia Dortmund winger Dembele had the final word.
Despite being down to ten men, France continue to dominate the game and they finally got their victor through Ousmane Dembele in the 78minute of the game.
The game had kicked off five minutes late due to a series of prematch tributes for the victims of the Manchester and London terror attacks, including the Republican Guard's rendition of Oasis' "Don't Look Back in Anger", a spirited, unified airing for the national anthems and a minute's silence.More news: Nadal reaches perfect ten at Roland Garros
"But the intensity and concentration levels, and the physicality, needed to stay with these teams I think in all three matches we have just faded in the end of those games".
Giroud leapt to meet Lemar's searching free-kick and Heaton could only shovel his header back in front of goal for Umtiti to pounce.
France wasted a glorious opportunity shortly after the quarter of an hour mark when Monaco's much-hyped teenager Kylian Mbappe hared down the left flank, only for his clever pass into the penalty area to be sliced wide by Dembele.
"I think both players had some really good moments and it's hard to assess without watching it back, but I thought there were definitely positive individual performances", he added.
"We've got to find a way to win, especially when they were down to 10 men". But we're very lucky we've got one of the best centre-forwards in the world at the moment in Harry Kane.More news: Ramallah movie theater follows Lebanon, bans Wonder Woman film
On an evening when only Harry Kane and Raheem Sterling resembled global players, Southgate was left looking for positives from another poor England performance. Their errors were punished by France who were down to ten men for nearly the entire second half.
Mbappe was thwarted again by Butland in stoppage time, although it is surely a matter of time before this brilliant talent scores the first of dozens of goals for France.
After the Paris attacks in 2015, England fans sang La Marseillaise at the game against France at Wembley.
"We need to see the reality of where we are and you have to play against the best otherwise it masks where you are as a team". Sometimes you have to keep adjusting, but good players are always going to test you, like France did today.
Kane, who hit an injury-time equaliser in Saturday's World Cup qualifier in Scotland, had taken just nine minutes to get his name on the scoresheet. What was more surprising was that, after consultation with the video referee, he then showed Varane a ridiculously harsh and frankly incorrect red card, before Kane scored from the spot.More news: Powerball numbers drawn for 10th largest US lottery prize