The gruesome Montreal investigation has attracted international attention, and police agency Interpol has put Luka Rocco Magnotta on the equivalent of its most-wanted list.
A senior French police official said Friday he is "sure" that Magnotta is currently in France, and said Magnotta has been to France in the past. Another French police official said Magnotta apparently flew to Paris from Montreal last weekend, before details of the suspected crimes emerged.
France's fugitive search unit has been ordered to hunt for Magnotta, the officials said. They spoke on condition of anonymity because they were not authorized to speak about such searches publicly. They gave no details about his suspected whereabouts within France.
Montreal police said Thursday that they believed Magnotta, 29, had fled North America based on evidence they found at his apartment and a blog he once wrote about how to disappear.
They suspect he killed a man he dated and filmed it. The video, posted online, shows a man stabbing another man with an ice pick while the victim lies naked and tied up. The first man later reveals he has slashed the other man's throat. He also dismembers the corpse and performs sexual acts with it.
Montreal police have been trying to take down the video.
The case began Tuesday when police found a man's torso in a suitcase behind Magnotta's apartment building and a severed foot was found in a package mailed to the Conservative Party headquarters in Ottawa. A hand was found in a separate package at a postal facility, addressed to the Liberal Party of Canada.
Other body parts remain missing.
Police believe the victim is a man reported missing several days ago and that the man's family lives overseas.
Police said Magnotta is also known by the names Eric Clinton Newman and Vladimir Romanov, and described him as white and 5 feet 8 inches tall (1.78 meters) with blue eyes and black hair. A police official said he was a porn actor.
Rob Gillies in Toronto contributed to this report.