Meeting Putin for the first time, Macron told a news conference that France and Russia must cooperate to "eradicate terrorist groups" in Syria and did not directly criticise Moscow's role there.
France and Russia back different sides in the Syrian conflict, with Putin supporting President Bashar al-Assad and Macron part of a western coalition that supports rebel groups and has accused Assad of using chemical weapons in the past.
"Our two countries will cooperate on Syria, this is essential," Macron said. "We need strong cooperation because we have a joint priority, which is the fight against terrorism."
Macron said he wanted Paris and Moscow to bolster intelligence sharing on Syria and to work together on finding a political solution to the conflict, but gave no details on what a political deal might look like.
Sounding less forthcoming, Putin said he wasn't sure if France's Syria policy was "independent" because it was part of a US-lead alliance, adding that Paris and Moscow had points of disagreement and agreement over Syria.
Putin said he and Macron had agreed the fight against terrorism was their top priority, but stressed that he hadn't changed his views on Syria.
Macron's warning of French retaliation in the event that chemical weapons are used echo the line taken by US President Donald Trump, who in April ordered cruise missile strikes in retaliation for a chemical weapons attack that Washington blamed on Damascus.
"Any use of chemical weapons would result in reprisals and an immediate riposte, at least where France is concerned," Macron said, standing next to Putin in the Versailles palace outside of Paris.
Both leaders called for an informal summit on Ukraine in the so-called 'Normandy Format' - a diplomatic group to resolve the conflict in eastern Ukraine made up of Russia, France, Germany and Ukraine.
A February 2017 ceasefire brokered between the government in Kiev and Russian-backed separatists in eastern Ukraine is being violated almost every day, with heavy weapons not withdrawn and other provisions not enacted.
Putin declared that the sanctions imposed on his country after the annexation of the Crimean peninsula - considered illegal by the UN - were "in no way" helping to end the fighting between government forces and Kremlin-backed rebels in eastern Ukraine.
But Macron said he would make "not a single concession" to Russia on the long-running conflict in Ukraine, with him and his G7 counterparts saying they were prepared to strengthen sanctions against Moscow.
Human rights, rule of law
The Russian president tried to shrug off allegations that Russian hackers infiltrated Macron's presidential campaign. "Maybe they were Russian hackers, maybe they were not," he said, dismissing the claims as unsubstantiated.
Macron, for his part, expressed anger at reports by pro-Kremlin media during the election questioning his sexuality and links to high finance. He took aim at the Russia Today broadcaster and Sputnik agency, calling them "organs of influence and propaganda".
The French president also referred to the repressive situation for gay people in Chechnya and that of NGOs in Russia. Macron told the media that Putin assured him multiple steps had been made to investigate claims of violence against gay people in Chechnya.
"I have made President Putin very well aware of what France’s expectations are", Macron said.