According to the Kremlin, both Putin and Macron called for experts of the International Atomic Energy Agency (IAEA) to inspect the plant "as soon as possible" and "assess the real situation on the ground."
"The Russian side confirmed its readiness to provide the Agency inspectors with the necessary assistance," the statement said.
In a separate statement, the French presidency said that Macron "supported the dispatch of a mission of experts from the IAEA to the site under conditions agreed by Ukraine and the United Nations."
It later specified that Putin had dropped his demand that the IAEA team travel to the site via Russia, saying it could arrive via Ukraine "in respect of Ukrainian sovereignty."
Putin and Macron will speak again "in the coming days on this subject after talks between the technical teams and before the deployment of the mission," the Elysee said.
Both Kyiv and Moscow have this week accused each other of preparing "provocations" at the facility.
The plant -- the biggest in Europe -- was targeted by several strikes in recent days, increasing fears of a nuclear disaster. Both Kyiv and Moscow have traded blame over the attacks.
Ukraine officials have opposed an outside inspection visit while the site is held by Russia, saying it would only "legitimize the occupation of the power plant."