The victim, identified to CNN as Imran Aliev, ran a YouTube channel criticizing the Chechen regime backed by Russian President Vladimir Putin.
French officials said Aliev, 44, "suffered a violent death."
Investigators believe he knew his killer, a source close to the investigation told CNN Tuesday.
According to the source, two individuals checked into the hotel room last Wednesday; on Thursday at approximately 11 a.m. local time the manager went to check on the guests and discovered Aliev's body.
The second man had disappeared. A manhunt is underway to find the 35-year-old Chechen man who police believe is the number one suspect, the source told CNN.
A knife found at the scene has been sent to a forensic laboratory for analysis, according to the source.
Police suspect motive is political
Police have launched a murder investigation, but no arrests have been made.
The source said police believe the motive for the killing may be political.
It is the latest in a number of high-profile murders of Chechen dissidents living in Europe in recent years, with rights groups warning the killings are a warning from Moscow.
Musa Taipov, a Chechen journalist who lives in France, pointed the finger at Moscow in a Facebook post about his friend Aliev's death.
"I strongly suspect Russia, in through its special services, extremely interested in the conflict, in the civil strife between the peoples of the Caucasus," he wrote on Facebook last week.
CNN contacted the Kremlin for comment, but had not received a response at time of publishing.
Aliev had four children and lived in Belgium, Taipov said, adding that he had been "in constant contact on WhatsApp," with him.
Murder a 'warning to others'
Mansur Sadulaev, who is chairman of the Chechen Human Rights Association (VAYFOND), based in Sweden, told CNN that Aliev was known for his "harsh and offensive remarks" about people of the Caucasus as well as his criticism of the Chechen regime.
Sadulaev also blames Moscow for the murder. "He was killed as a warning to others, thus trying to intimidate everyone who criticizes 'Russian protégé' in Chechnya Ramzan Kadyrov."
Kadyrov is a former warlord known for his brutality -- and for his allegiance to Russian President Vladimir Putin.
"Opponents of the Russian regime and supporters of the independence of the Chechen Republic, especially those who express themselves openly, are in constant danger both in the EU and in any other country," Sadulaev said.
"Among the many murders and murder attempts on opponents of the Russian regime there is the recent assassination of Zelimkhan Khangoshvili in Berlin," Sadulaev added.
Chechen dissident Zelimkhan Khangoshvili was shot and killed in Berlin in August while on his way to midday prayers at a nearby mosque.
Khangoshvili had fought in the second Chechen war, alongside fellow Chechen insurgents against Russian federal forces. A suspect, who was carrying a Russian passport, was arrested within hours.