French president Emmanuel Macron says he held a "frank exchange" with Russian counterpart Vladimir Putin in their first face-to-face talks, reports the BBC.
The pair discussed "disagreements" in the meeting, held at the sumptuous Versailles palace.
But Mr Macron said he wanted to work with Russia over Syria in the struggle against terrorism.
Meanwhile, Mr Putin said he wanted to strengthen economic ties with France after the restrictions of recent years.
Both leaders were keen to signal a new beginning in Russian-French relations that have been under considerable strain recently, says the BBC's Hugh Schofield in Paris.
Tensions have risen over the conflicts in Ukraine and Syria, where France and Russia back opposing sides.
And Mr Macron's election team accused Russian agents of launching cyber attacks against them during his campaign for the presidency.
Mr Macron has previously spoken of the importance of speaking to Russia, but said that he expected some tough words.
At the G7 summit in Sicily at the weekend he 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.