Didier Deschamps' men, runner-up at their home European Championship two years ago, enter the World Cup in Russia as one of the favourites.
That is in part thanks to Griezmann, the Atletico Madrid forward having top-scored at Euro 2016 with six goals.
Mbappe, another one of France's attacking talents, said Griezmann had already shown he could lead his nation at a major tournament.
"I think that he is the boss since the Euro already," Mbappe said. "When you end the European Championship the best goal-scorer in your own country, you show the world that you have the shoulders to handle the pressure.
"It's true that he went through a bad patch following the competition but he showed how [much of] an amazing player he was and he is by scoring goal after goal.
"He will be pivotal for us if we want to get results."
France begins its Group C campaign against Australia before meetings with Peru and Denmark.