France are aiming to win gold for the second time, 40 years after their triumph in Los Angeles, and will face Spain in the final after narrowly avoiding a shock defeat against Egypt on Monday.
Henry's team were trailing 1-0 in the semi-final in Lyon but came back to win 3-1, with Jean-Philippe Mateta equalising to force extra time and then scoring again in the 99th minute before Michael Olise sealed the victory.
"I am going to be honest, I am mainly happy for Team France because when you see everyone picking up medals all over the place, you say to yourself that you can't let them down," Henry said.
"You don't want to be the team that doesn't win a medal, so at least that is done, and now we will see what colour we get.
"But honestly I am living a dream and I don't want to wake up."
Henry, who won the Champions League with Barcelona and both the World Cup and European Championship with France as a player, was appointed coach of France's Under-21 and Olympic teams just under a year ago.
The 46-year-old will now lead them out on Friday in the final at the Parc des Princes, the same ground where France beat Spain in the final of the 1984 European Championship just weeks before their only Olympic victory to date.
"You know how difficult it is going to be against them. They are often in the finals of competitions, in both men's and women's football," Henry added of the Tokyo Olympic silver medallists who beat Morocco 2-1 in their semi-final.
France are guaranteed a medal after making the final despite failing to enrol the services of full national team captain Kylian Mbappe and vice-captain Antoine Griezmann for the Olympic tournament.
Instead they have been led from the front by Lyon's former Arsenal striker Alexandre Lacazette, while their star man in the knockout rounds has been Mateta.
He scored 16 goals in the Premier League last season for Crystal Palace, including 14 in his last 16 games.
Now he is France's top scorer at the Games with four goals, among them the winner in a fiery quarter-final against Argentina and his double against Egypt.
"It is a dream to be in the final and I can't wait to be in Paris," said Mateta, who comes from the suburbs of the French capital.
"We have been talking about the Games for a year and a half now and finally we get to go to Paris."
