Mittenaere beat Miss Haiti, first runner-up, and Miss Colombia, second runner-up, to win France's fist Miss Universe title since 1953, the year after the pageant was started in the US to compete with Miss World, a British initiative.
"I was very surprised," Mittenaere told the press in the Philippine capital, Manila, where the event took place. "I am always touching the crown and saying 'Oh my God. I have the crown on my head. I don't believe it."
She said she would work for good hygiene and children's education.
When asked about the global refugee crisis, Mittenaere said France had the right to close its borders to refugees but spoke of the benefits of migration.
"In France we want to have the most globalisation that we can," she told the MC. "We want to have the biggest exchange of people that we can. Maybe someday that will change but now we have open borders.
"Having open borders allows us to travel more through the world and to find out more about what's out there in the world."
Miss Universe is open to women between 18 and 24 years of age who are single, have no children and have not posed naked.