"In France, the mercenary trade is forbidden by law," the State Duma's chairman said.
A network of bots that prosecutors believe is controlled by the Russian mercenary group Wagner Force promoted photos of spray-painted stars on social media, a French official said.
US officials are unable to confirm that the system has been sent yet, but noted a positioned aircraft carrier used to deter Hezbollah in the Eastern Mediterranean.
One Telegram channel which calls itself CHVK posted a sarcastic montage of Prigozhin's own voice saying: "Well of course, we sniffed a load of coke and then threw some grenades about on the plane."
Putin suggested the plane was blown up from inside, saying that the head of Russia's investigative committee had reported to him a few days ago.
Putin's Kremlin meeting with Wagner's Troshev, who now works for the defense ministry, is a major hint that Wagner fighters - if not the group itself - are returning to the war.
"We have recorded the presence of a maximum of several hundred fighters of the former Wagner PMC (private military company)," Serhiy Cherevatyi, spokesperson for the eastern military command, said.
Russian President Vladimir Putin is suspected of being behind the death of rebellious Wagner Group leader Yevgeny Prigozhin.
Zelensky made the comment in passing at a conference in Kyiv as he was asked a question about the Russian president.
The draft order will allow Wagner's assets to be categorized as terrorist property and seized, BBC said, adding that it will be illegal to be a member or support the organization.