Putin's visit is seen as the latest test of the new French president's mettle after the G7 and NATO summits.
French President Emmanuel Macron greeted his Russian counterpart Vladimir Putin in the splendour of the Versailles palace outside Paris on Monday for their first face-to-face talks.
Macron and Putin, who have clear differences on Ukraine and Syria, are to hold a news conference after their talks.
Both leaders will also inaugurate an exhibition marking 300 years since Russia's modernising tsar, Peter the Great, visited France in 1717.
Putin's visit is the latest test of Macron's diplomatic mettle after the G7 talks in Sicily last week and the NATO summit in Brussels, where he turned the tables on Trump by refusing to release the American leader's hand for several seconds during the handshake for the cameras.
"It is essential to talk to Russia because there are many international issues that will not be resolved without a tough exchange with the Russians," Macron said in Sicily.
Russia's powerful ambassador to France, Alexander Orlov, said he hoped the meeting could help turn the page on the fraught relationship between Putin and Macron's predecessor Francois Hollande.
"Many things in the future will depend on the first meeting," Orlov told Europe 1 radio.
"It is very important that we begin to dissipate the mistrust that has built up in recent years."
Tough words for Russia
As a candidate, Macron had tough words for Russia, accusing it of following a "hybrid strategy combining military intimidation and an information war."
Since the start of the war in Ukraine in 2014, Russia has flexed its muscles with a series of war games involving tens of thousands of troops in areas bordering NATO Baltic states.
Macron told a French weekly that he was "not bothered" by leaders who "think in terms of power ratios," citing Putin as an example along with Trump.
But Macron, who became France's youngest president just three weeks ago, said he does not believe in "the diplomacy of public invective but in bilateral dialogue."