Azoulay told French radio on Monday that the United Nations Educational, Scientific and Cultural Organisation (Unesco) had survived long periods without Washington before.
The former French culture minister said the US was "not the beginning and end" of the agency.
The US and Israel both announced their withdrawal last month, accusing Unesco of "anti-Israel bias".
"It's a sovereign decision by a state that I respect, but which at the same time is not the beginning and end of Unesco," she said.
"There have been long periods at Unesco -- more than 15 years -- without the United States, which ultimately came back."
She added that Unesco would continue "working with American civil society, American universities and American scientists".
The United States' troubled past with Unesco
The US walked out of the 195-member organisation once before in 1984 over alleged financial mismanagement and claims of anti-US bias.
It returned in 2002, but in 2011 former president Barack Obama cut off funding after Unesco's members voted to admit Palestine as a full member.
US ally Israel similarly pulled the funding plug, leaving Unesco short of more than 20 percent of its budget.
Both countries announced on 12 October that they were leaving the organisation outright after a series of resolutions condemning Israel.
Best known for its World Heritage sites including the Grand Canyon and the Great Wall of China, Unesco promotes education and pushes for improvements on social issues such as gender equality.