"To rebuild unity, we must promote UNESCO's assets and know-how and that of its members," Azoulay told AFP in an interview.
The Paris-based cultural, scientific and cultural organisation "must show through its actions that UNESCO is addressing the challenges of globalisation today," said the 45-year-old whose nomination was confirmed on Friday.
She said she would seek to "reduce a certain amount of tensions" but conceded that they would "always exist".
In 2011 US president Barack Obama suspended funding for UNESCO -- about 22 percent of its annual budget -- for accepting Palestine as a member.
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In the years since, UNESCO has been the scene of several flare-ups over Arab-sponsored resolutions critical of Israel.
In July, it declared the Old City of Hebron in the occupied West Bank an endangered World Heritage site, infuriating Israel while delighting Palestinians.
"But UNESCO must keep the door open and continue to work with American civil society," said Azoulay, who was culture minister under the Socialist president Francois Hollande for a little over a year until he left office in May.
"We must nip divisive issues in the bud, find joint solutions" and avoid issues that UNESCO cannot resolve -- "which is not its function by the way", Azoulay said.
Azoulay said UNESCO's budget integrates both dues and voluntary contributions and is "realistic".
"As for the current budget, we must determine the most crucial areas for action by UNESCO, where it is the only one acting, and adapt our priorities to our means."
The agency can also "maybe get support from other networks, other partnerships," she said.
Asked about UNESCO's image as a second-tier UN agency that is mainly concerned with developing its prestigious World Heritage list, Azoulay said that view was "very French".
Azoulay added: "Education is the main challenge of our century; it is fundamental. UNESCO may have a lower profile than other agencies because it doesn't build schools, but it is the world reference on the substance, the content of education," she said.
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