In a statement Macron paid tribute to the "historic role" Barzani has played as president of Iraqi Kurdistan and his role in fighting the Islamic State (IS) armed group "to which the Peshmerga [Kurdish fighters] have brought a determining contribution".
But, with Iraqi central government troops seizing territory from the Peshmerga following the Kurds' independence referendum, Macron is clearly concerned that the fighting will disrupt the final effort to deprive IS of the last territory it holds.
He called on "the Kurdistan regional govenrment and the Iraqi federal authorities to abstain from all military operations and to return to dialogue, with the support of the United Nations, so as to reach a lasting peace in a united Iraq".
The statement is Macron's second call for dialogue since the two sides started fighting.
"France will continue to work to facilitate this dialogue in the coming weeks," the statement added.