"To rebuild unity, we must promote UNESCO's assets and its know-how, as well as 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 tension" but conceded that difficulties would "always exist".
The vote that saw Azoulay succeed outgoing UNESCO chief Irina Bokova was somewhat overshadowed by Washington's announcement that it planned to withdraw from the body after years of strained relations over decisions seen as critical of Israel.
In 2011, former US president Barack Obama suspended funding for UNESCO – about 22 percent of its annual budget – in response to its decision to admit the state of Palestine as a full member.