The trip is Macron's first to Russia as president and follows a visit by German Chancellor Angela Merkel last week. Europe and Moscow are making diplomatic overtures to save the Iran deal, now under threat after the recent US withdrawal.
The French and Russian leaders will “take the time for an in-depth one-on-one discussion”, according the Elysee.
Macron will be accompanied by his wife Brigitte during the trip, which will also see him address the Saint Petersburg International Economic Forum.
The meeting comes almost exactly a year since the freshly elected Macron hosted Putin in Versailles, when the French leader accused Russian media of producing “lying propaganda” during a joint press conference.
This time Putin will welcome the French president to the Konstantin Palace, a former residence of Peter the Great set some 20 kilometres (12 miles) outside Saint Petersburg.
The talks take place after President Donald Trump in early May controversially pulled the US out of the 2015 landmark pact with Iran that placed limits on its nuclear programme in return for easing economic sanctions.
Washington is threatening stinging fresh sanctions if Tehran does not comply with a set of strict new demands.
Saving the deal provides a rare point of agreement between Moscow and European countries, which have seen relations tank in recent years over crises in Ukraine and Syria, as well as accusations of meddling in foreign elections and the poisoning of an ex-Russian spy in Britain.
“Russia shares the position of the majority of the international community including Western leaders” when it comes to the Iran deal, said Alexander Baunov of the Carnegie Moscow Center.
The West has realised that a dialogue with Putin is “inevitable” in order to preserve the accord, he said.
Japanese Prime Minister Shinzo Abe will also visit Russia at the end of the week.
“Merkel and Abe have already begun a thaw with Moscow and Macron is scared of losing the advantage that France has always had with Russia,” Baunov added.
But there are a number of sticking points that will prevent a full rapprochement between Paris and Moscow.
Chief among them is Syria, where at least 350,000 people have been killed since war broke out in 2011.
Moscow intervened in 2015 to prop up its ally President Bashar al-Assad — in a move generally seen as decisive in turning around the multi-front
conflict — while France has participated in strikes on regime targets.
Another issue is the conflict in eastern Ukraine, which broke out after Russia annexed Crimea in 2014 and has so far claimed at least 10,000 lives.
Paris and Moscow, along with Berlin, signed peace agreements in Minsk in 2015 that aimed to bring the fighting to a close but there is currently no end in sight.
On Wednesday, Human Rights Watch also implored Macron to raise the issue of rights abuses with his Russian counterpart, following a crackdown on dissent and pressure on minority groups in the country.
He must confirm “that the France will never accept the increased repression in Russia as 'the new normal',” the NGO said in a statement.
But the talks between the two presidents will not be the only bilateral activity of the day, as a raft of commercial agreements are also set to be signed during the economic forum.
The presence of the French president at the forum “legitimises visits by business people. Those who are worried about the risks, sanctions or criticism are covered to a certain extent by the president,” analyst Baunov said.
“If anything, the political leadership will get criticised for this rapprochement and not the business community.”