He had been due to meet French President Francois Hollande and open a new Orthodox church later this month.
But after France's government said talks would be confined to Syria the visit was halted, French presidential sources said.
On Monday, Mr Hollande suggested Russia could face war crimes charges over its bombardment of Syria's city of Aleppo.
The French presidency had told the Russians Mr Hollande would attend only one event with Mr Putin during the visit planned for 19 October - a working meeting on Syria, according to the sources.
But after this Russia "let it be known that it wanted to postpone the visit", they added.
A Kremlin source cited on Russian state media confirmed the meeting would not go ahead.
It comes a day after Mr Hollande told French TV prosecutions over Syria could take place in the International Criminal Court (ICC).
"These are people who today are the victims of war crimes. Those that commit these acts will have to face up to their responsibility, including in the ICC," he said.
Neither Russia nor Syria is a member of the ICC.
Moscow has repeatedly denied attacking civilians, and says it targets terrorist groups in Syria.
Last week Russia vetoed a UN Security Council resolution drafted by France calling for an end to the bombing in Aleppo.