Winger Dembele sealed the victory with an angled shot from inside the box 12 minutes from fulltime after being nicely set up by fellow youngster Kylian Mbappe.
England captain Kane put them ahead from close range from a low Ryan Bertrand cross before the 10-minute mark and levelled the game at 2-2 with a penalty early in the second half after Varane was sent off for bringing down Dele Alli in the box.
France had fought back to lead 2-1 at halftime, after defenders Samuel Umtiti and Djibril Sidibe each scored their first goal for their country.
The two efforts were similar, with Umtiti and Sidibe both following up to finish after saves by England goalkeeper Tom Heaton, first from an Olivier Giroud header, then from a shot by Dembele.
Kane, who struck the late equaliser in a 2-2 draw with Scotland in a World Cup qualifier on Saturday, has now scored 11 goals in his past five appearances for club and country combined. It was not enough, however, to deny a spirited and daring French side.
"We saw in that game the things we're very good at and equally the things we need to get better at, like defending as a team and managing a result," England coach Gareth Southgate told a news conference.
PROMISING TRIO
France coach Didier Deschamps, who was criticised for conservative tactics in a 2-1 defeat by Sweden in a World Cup qualifier on Saturday, revamped his team to put exciting newcomers Mbappe, Thomas Lemar and Dembele in his starting lineup.
The trio gave the England defence a hard time on several occasions, notably Mbappe, who rattled the crossbar with a curled left-foot shot shortly before setting up Dembele for his maiden goal for France.
"We scored a goal with 10 men against a good England side, which is quite an achievement," Deschamps told a news conference. "The players looked fresher and showed more initiative than against Sweden."
Tuesday's match, which was attended by French President Emmanuel Macron and British Prime Minister Theresa May, was the first senior England fixture with a video assistant referee, who was consulted for Varane's red-card offence and the penalty that resulted from it.
Prior to kickoff, fans at the Stade de France paid tribute to the victims of the recent militant attacks in Manchester and London.
The Oasis song "Don't Look Back in Anger" rang out as the teams emerged from the tunnel, with fans holding up red and white placards to form the England flag.
(Editing by Toby Davis)
