Jihadist propaganda was posted on the station's website in April by individuals claiming to represent Islamic State.
A police investigation is now focussing on a group of Russian hackers called APT28, according to French media.
The group has tried to hack the White House in the past, L'Express reports.
It has also targeted the computer systems of Nato members, Russian dissidents and Ukrainian activists, according to the newspaper.
A judicial source told AFP that investigators were narrowing the search by probing the IP addresses of computers used in the attack.
TV5 Monde was forced to broadcast pre-recorded programmes after the hack, which it described as "unprecedented in the history of television".
A message warning French troops to stay away from Islamic State was published on the station's Facebook page.
The hackers also posted documents purporting to be ID cards of relatives of French soldiers involved in anti-IS operations.
A cyber attack on the French television network TV5 Monde may have been carried out by Russian-based hackers, police believe.