TF1 TV, citing anonymous sources, reported that Pavel Durov, the billionaire co-founder and CEO of messaging app Telegram, was arrested on Saturday evening at Bourget airport outside Paris.
TF1 reported on its website that Durov was traveling on a private jet and that an arrest warrant had been issued in France.
The 39-year-old man, believed to have been travelling from Azerbaijan, was arrested at around 8pm local time (6pm GMT).
Durov is due to appear in court on Sunday.
The Russian-born entrepreneur lives in Telegram's home base in Dubai and holds dual French and UAE nationality.
Durov, whose fortune is estimated by Forbes magazine to be $15.5 billion (£12 billion), left Russia in 2014 after refusing to comply with demands to close opposition communities on his social media platform, VK, which was then sold.
Telegram did not immediately respond to a Reuters request for comment.
The Russian embassy in France said it was taking “immediate steps” to clarify the situation.
TASS, citing a representative of the Russian embassy in France, said that no complaint had been filed by Durov's team with the embassy, but that the latter was actively taking “immediate” measures.
Durov and his brother Nikolai founded the messaging app in 2013 and it now has around 900 million active users.
Telegram offers end-to-end encrypted messaging and also allows users to set up “channels” to quickly disseminate information to their followers.