France's Macron holding 'tough' talks with Putin near Paris
It could be an awkward meeting, the BBC's Lucy Williamson in Paris reports.
Recently Mr Macron's election team accused Russian agents of launching cyber attacks against them.
At the G7 summit in Sicily at the weekend Mr Macron said: "It is essential to talk to Russia because there are a number of international issues that will not be resolved without a tough dialogue with them."
France is in the coalition backing Sunni Arab and Kurdish rebels opposed to Syrian President Bashar al-Assad, who has strong military help from Russia and Iran.
France has taken a firm line against Moscow over Russia's intervention in Ukraine. Western sanctions, imposed after Russia's annexation of Crimea in 2014, have been ratcheted up since pro-Russian rebels carved out a breakaway region in eastern Ukraine.
Ties between Russia and France became strained under Mr Macron's predecessor François Hollande.
President Putin cancelled a visit to Paris in October after President Hollande said Russia could face war crimes over its actions in Syria.
Mr Hollande also reportedly refused to take part in the opening of the newly built Russian Orthodox Spiritual and Cultural Centre in Paris, which Mr Putin is due to belatedly visit after meeting Mr Macron on Monday.
Image caption Marine Le Pen had an audience with President Putin in Moscow in March
Mr Putin appeared to support Mr Macron's nationalist rival Marine Le Pen during the French presidential election campaign.
He hosted Ms Le Pen in the Kremlin a month before the election's first round.
Ms Le Pen's National Front (FN) has received significant loans from Russian banks or banks associated with Russian financiers. She argued that French banks would not give the FN any loans.
Before becoming president this month Mr Macron accused Russia of pursuing "a hybrid strategy combining military intimidation and an information war".
Versailles was chosen for the Macron-Putin meeting because an exhibition dedicated to Tsar Peter the Great is opening there. He visited Paris 300 years ago, along with other European countries which greatly influenced his reign.
It is President Macron's latest diplomatic test after the G7 talks in Sicily and the Nato summit in Brussels where he turned the tables on US President Donald Trump by holding him in a clenched handshake until their knuckles went white.
Afterwards, Mr Macron told French media the exchange was "not innocent" and he had wanted to "show he would not make small concessions, not even symbolic ones, but also not overdo things".