Russian newspaper Novaya Gazeta reported in March that the authorities in the Muslim-majority Caucasus region were imprisoning and torturing gay men.
More than 100 gays had been arrested in the region, where homosexuality is taboo, two people had been killed by relatives and a third died after torture, it reported.
Macron said Putin, who agreed to back an investigation into the claims after meeting German Chancellor Angela Merkel earlier this month, promised "the whole truth" about the reported persecution when they met and the French presient insisted France would be "vigilant" on the issue.
But Russian Foreign Affairs Minister Sergei Lavrov on Tuesday insisted there were "no facts" to back up the reports.
Azmad, the first person to be allowed to come to France on the basis of the reports, arrived on the same day as Macron met Putin.
The 26-year-old was granted an "emergency humanitarian visa" last week, according to Joël Deumier of French gay rights campaign SOS homophobie.
Other cases are being examined, he said.
Persecution started last winter
Azmad (not his real name) fled Chechnya after police demanded he hand over and unlock his phone so as to examine his contacts and photos.
They had tracked him down because his photo was in an associate's phone.
With the help of a friend, he ran away to Moscow, where he was in hiding for two months.
Talking to the AFP news agency, he backed up Novaya Gazeta's report.
Last winter the body of one man was found "naked and tied up" after having been "raped and killed", he told the AFP news agency after arriving in Paris.
Since then the police have been seeking out gays, he said, and the persecution became intense.
"If it becomes known you're in danger and so are people close to you," Azmad said. "They kill people over a rumour there."