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.

The double Olympic champion clocked the fastest time in the world this year, winning in seven minutes 34.66 seconds
"The crowd have been amazing, as has the support I have got for the last few months," Farah, 32, told BBC Sport.
He was running in England for the first time since allegations of doping were made against coach Alberto Salazar.
Salazar denies the claims while Farah himself is not accused of any wrongdoing.
Briton Farah withdrew from June's Diamond League meeting in Birmingham following the accusations against his coach, stating he was "emotionally and physically drained", but went on to win the 5,000m race in Lausanne earlier this month.
He was given generous applause from the crowd inside the arena when his name was announced at the start and the Somalia-born athlete responded with a smile and his trademark 'Mobot' gesture.
Having celebrated wildly when winning in Switzerland, he showcased Usain Bolt's celebratory pose after the finish line, in homage to the Jamaican who won the 100m event.
"I was pleased with tonight," added Farah. "I felt a bit tired at the start but you have to win the race and not to think about the time.
"You can only do what you do best. For me, that is running. It is great for the people to understand and support me.
"It was great memories from 2012 and I saw Usain Bolt win before me. We take it for granted what he does, to come out year after year and keep winning medals."
Farah took the lead after the 2,000m mark, controlling the pace of the race, and he opened up a comfortable gap before sprinting the last 200m in 26.5secs.

Dan Biggar was heard querying whether to kick for the corner when Wales won a penalty while trailing 16-13 but denied he overruled Jones' decision.
Leigh Halfpenny admitted he turned down the chance to kick at goal, however.
"Things happen on the field which challenge everybody at the best of times," Thorburn told BBC Radio Wales.
He continued:  "I don't think it questions his ability as captain at all.
"Alun is unquestionably one of the most inspirational players that has been around in the Welsh camp for a long time."
Thorburn says he would have no reservations over picking Jones as captain of the British and Irish Lions in light of Wales' poor start in the Six Nations.
"He [Jones] leads from the front," he said.
"Are you going to base it on the argument about Dylan Hartley, the England captain, whose team didn't know how to cope with some bizarre scenarios against Italy on Sunday?"
Wales could have levelled the scores at 16-16 from the penalty if they had kicked for goal instead of the corner, but Thorburn says it is the kicker's responsibility to decide what happens, not just the captain's.
"I've been on both sides of the fence - a captain and the goal kicker - what we don't know is what the conditions were like on the field," Thorburn added.
"The wind does swirl around Murrayfield and I suspect Leigh probably thought that it was going to be a long kick into what would be a very difficult conditions.
"The issue is whether Alun, as captain, should have consulted with him first. We can argue about that until the cows come home but ultimately the kicker is the one who is taking the shot and has to be comfortable."
A cyber attack on the French television network TV5 Monde may have been carried out by Russian-based hackers, police believe.
[NEXT_CONCEPT]
Britain's Mo Farah received a raucous reception as he eased to victory in the 3,000m at the Anniversary Games in the Olympic Stadium, London.
[NEXT_CONCEPT]
Former Wales skipper Paul Thorburn says there is no question over Alun Wyn Jones' captaincy despite claims he was overruled in the loss to Scotland.