Azoulay, who served as a minister under President Francois Hollande, narrowly beat Qatar’s Hamad bin Abdulaziz al-Kawari in the final 30-28 vote on Friday.
Azoulay must be approved by UNESCO’s 195 members on November 10.
The 45-year-old will succeed Irina Bokova, a Bulgarian who has led the body since 2009.
The voting comes a day after the United States announced that it will withdraw from the UN’s cultural organization, accusing it of “anti-Israel bias.”
US State Department spokeswoman Heather Nauert said in a statement on Thursday that Washington would establish an “observer mission” to replace its representation at the Paris-based agency.
“In this time of crisis we need more than ever to support, strengthen and reform UNESCO and not leave it,” Azoulay told journalists, saying she would modernize the agency.
“If I’m confirmed…the first thing I will do is to restore its credibility, restore the faith of its members and its efficiency so it can act,” she added.
UNESCO is known for designating world heritage sites such as Syria’s Palmyra, the Grand Canyon in the US state of Arizona and twenty-two sites in Iran.