Sheikh Abdullah wished Ms Colonna success in the role and highlighted the deep ties between the nations during a phone call, state news agency Wam reported.
The two ministers exchanged views on a range of regional issues and discussed ways to strengthen international security and stability.
They explored joint efforts to combat climate change in light of the UAE's hosting of the 28th session of the Conference of the Parties, more widely known as Cop28, next year.
The climate conference will be held at Expo City Dubai, the President, Sheikh Mohamed, said last week.
The meeting of world leaders in November 2023 will seek to find solutions to the dangers of climate change.
Ms Colonna took on her new ministerial position last month.
She had previously served as French ambassador to the UK, Italy and San Marino and as representative to Unesco.