The refugee's arrival was confirmed by Joël Deumier, president of French gay right's group SOS Homophobie, who said more may follow in the coming days.
Deumier announced the arrival of the refugee from Chechnya, where gay men have allegedly been tortured and their families told to kill them, on the same day Russian leader Vladimir Putin visited Paris to hold talks with his French counterpart Emmanuel Macron.
Macron said on Monday that Putin had promised "the whole truth".
"President Putin told me... he had undertaken several initiatives on the subject of LGBT people in Chechnya with measures aimed at establishing the whole truth about the activities of local authorities," Macron said at a press conference with Putin after talks in Versailles.
"I spelled out France's expectations very precisely," Macron said, adding that he would be "vigilant" on the issue and that the two leaders had agreed to review the situation regularly.
Russian newspaper Novaya Gazeta reported in March that authorities in Muslim-majority Chechnya were imprisoning and torturing gay men.
It said that over 100 gays had been arrested in the region, where homosexuality is taboo, and that their families have been told to kill them to "cleanse their honour".
The paper said at least two had been killed by relatives and a third died after being tortured.
Earlier this month Putin backed an official probe into the reported attacks after German Chancellor Angela Merkel confronted him on the issue during a visit to Moscow.
But SOS Homophobie dismissed Putin's claims of an investigation into the 'LGBT purge' in Chechnya.
"We hear Mr Putin say that he has launched an investigation, that it is not true and that there are no crimes against homosexuals, which is totally false," said the organisation's leader Joël Deumier.
"We can no longer accept this discourse of negation by Russia against homosexuals."
Coinciding with Putin's visit to France on Monday, two gay couples unfurled a banner reading "End Homophobia in Chechnya" and kissed with the Eiffel Tower in the background.