Alexander Baunov, a senior fellow at the Carnegie Moscow Center, said Macron would be looking for ways to resuscitate the 2015 Minsk ceasefire deal which Paris and Berlin helped broker.
"The relation of France and Russian Federation, of Russia and the European Union is absolutely decisive", Macron said.
Pressed by reporters over the Russian authorities crackdown on opposition protests in Moscow, Putin said he did not want a situation like the French "yellow vests" to arise in the Russian capital.
"Putin said Moscow does not want protests like the" yellow vest" ones that have taken place in France, but that peaceful demonstrations were welcome. "Of course, we will support it". "We never said that in Idlib terrorists would feel comfortable", he added.
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The Normandy Format meeting may be held in next weeks, - Macron
But he said that phone conversations with Ukrainian President Volodymyr Zelenskiy had given him "cautious" grounds for optimism. Macron said the comparison with France was inaccurate, since at least yellow vest protesters could stand in elections.
Zelenskiy's election in April "gives us some room to maneuver", the official added.
"We will discuss this situation and, perhaps, prepare future meetings with (German) Chancellor (Angela) Merkel and president Zelensky in the Normandy format", he said.
At a meeting with Macron, the heads of state discussed rallies in Moscow, the war with Ukraine, Russia's return to the G8, and other global problems.
The relationship between a youthful French leader who regards himself as a champion of European liberalism and Putin, in power for two decades, has been marked by wariness and tensions.
The presidents had a meeting, followed by a dinner at the southern France palace, which the first lady reportedly attended.
But Putin said Russian Federation, which entered the conflict in 2015 in support of the regime of President Bashar al-Assad, backed the Syrian army's operations in Idlib, which is the last major jihadist-run bastion in the war-torn country.