Conditions at Europe's biggest nuclear power plant continue to cause global concern.
Russia and Ukraine accuse each other of shelling around the Zaporizhzhia plant and risking a catastrophic release of radiation.
Statements from the Kremlin and the Elysee Palace highlighted the difficulties in trying to find an accord to ensure safety at the site.
"The Russian side drew attention to regular Ukrainian attacks on the plant's facilities, including radioactive waste storage, which is fraught with catastrophic consequences," the Kremlin said.
Zaporizhzhia nuclear power plant attacked - in pictures
It called for a "non-politicised interaction" on the matter with the participation of the International Atomic Energy Agency.
But the French presidency said the occupation by Russian troops of the plant was what was putting it at risk.
"He [Macron] asked that Russian forces withdraw their heavy and light weapons from it and that the IAEA's recommendations be followed to ensure safety at the site," the Elysee said.
The IAEA has called for a security zone to be established around the site.
IAEA issues warning over military activity near Zaporizhzhia - video
On Sunday, the agency said a back-up power line to the plant had been restored, providing it with the external electricity it needs to cool its reactors and defend against the risk of a meltdown.
State agency Energoatom had earlier said it halted operations at the plant as a safety step.
Mr Macron would remain in contact with Ukrainian President Volodymyr Zelenskyy "as well as the director general of the IAEA, and will speak again in the coming days with President Putin so that an accord to guarantee security at the power plant can be found", the Elysee said.