The decaying torso of Caroline Corvalan, who had worked as a freelance journalist for French public television, was found at the end of September in a service duct by workers at a construction site.
Investigators last week identified someone close to the victim as a person of interest, but it was unclear whether that person was among the four arrested.
Numerous theories have circulated about the case, but investigators have been focusing on Corvalan's private life.
'Psychological problems' and a mysterious robbery
According to Metro News, Corvalan had been working for France Television in Cannes, on the French Riviera.
She was reported missing on August 20th, and her employer France 3 and her family both said they had not heard from her in a long time. According to Le Parisien, the journalist had been on sick leave for several months, due to “psychological problems”.
Police sources also told Le Parisien they were investigating a mysterious burglary at the woman’s home in the 18th arrondissement.
“On September 18th, one or more strangers went into her home to steal her phone, a digital tablet and her purse,” a source close to the case told Le Parisien. “Those close to her thought she had gone back to pick up her things before leaving.”
Police then noticed that a camera, which was not in her apartment several days before the burglary, then mysteriously reappeared.
“The camera is currently being examined, but for the moment we cannot explain this strange fact,” a source told the paper.
The remains of Corvalan were discovered near Bichat hospital, where she had reportedly received treatment for "mood disorders". She was identified only through her fingerprints.
Friends and family have paid tribute to the woman, who is originally from Alpes-Maritimes region of southern France.
“She had a huge heart and helped many homeless people. She suffered a lot in this life. She was such a lovely person, always sensitive and always spoke from the heart,” said her father.