According to a story in the London Times, French police are looking for Ian Griffin, who witnesses say drove away from the Hotel Bristol in a Porsche sports car just before the body was found in what appeared to be a violent scene.
"The autopsy showed that she died of blows to the body. There was no weapon used except for bits of furniture and fists," a French official told the London Times.
Police have identified the victim as Kinga Legg, a 36-year-old businesswoman.
Rooms at the Hotel Bristol cost from 500 Pounds, around $800 U.S., a night. It is one of Paris' most affluent places to stay.
The Hotel Bristol is one of Paris' most posh hotels, where rooms cost $800 and up.