French President Emmanuel Macron told Russian President Vladimir Putin that he must respect democratic principles as the leaders held a joint press conference in France.
The two leaders addressed the media ahead of talks at Fort de Brégançon, a medieval fortress and the President's retreat off the French Mediterranean coast.
While the G7 kicks off in Biarritz at the weekend, Putin will not attend after Russia was suspended in 2014 over its annexation of Crimea from Ukraine.
Macron called for the respect of free speech and free elections in Russia.
"We called this summer for freedom of protest, freedom of speech, freedom of opinion and the freedom to run in elections, which should be fully respected in Russia like for any member of the Council of Europe," he said. "Because I believe in a European Russia."
Putin retorted that he did not want a situation like the Gilets Jaunes protests his own country and said those who are guilty of breaking protest laws should be held responsible.
Macron said he hoped to discuss the crises in "of course" Ukraine, as well as Syria and Libya because "Russia has an essential role in these situations".
The French leader said he hoped talks with Putin would lead to a leaders' summit on the crisis in Ukraine over the coming weeks.
Putin said the two leaders would discuss his recent talks with Ukraine's new President Volodymyr Zelensky, which he said provided "cautious grounds for optimism".
He nevertheless stressed he would support Normandy format talks — a diplomatic group of senior representatives of four countries (Germany, Russia, Ukraine and France) to resolve the war in Eastern Ukraine — and that there was no alternative to it.
When a journalist asked about the G7 summit — formerly the G8 until Russia was suspended in 2014 — Putin responded that the "G7 doesn't exist".
"How can I come back to an organisation that doesn't exist," he said, adding while the G7 leaders were welcome in Russia, there are other international organisations that include countries like India and China too.
Macron reasoned: "It's not today that we are going to resolve misunderstandings that were installed back in the 90s."
The French head of state has faced criticism for inviting Putin to France at a time when Moscow has crushed opposition protests and remained uncompromising over Crimea and Syria.