76-year-old Claude Dray lived with his wife, Simone, in the wealthy western suburb of Neuilly-sur-Seine where Nicolas Sarkozy was mayor for 19 years.
He was found dead in his home, the Villa Madrid, a listed building. His wife was travelling in the US at the time.
Dray was last seen alive at around 11pm on Monday evening by his butler, reported Le Parisien newspaper.
Some time between then and the next morning he was shot three times. His body was found by his butler in his bedroom.
The newspaper reported that police found no evidence of a break-in or signs of a struggle at the luxurious home.
"We haven't yet established whether there was a burglary at the house," said a police source quoted by the newspaper. "The weapon has not yet been found."
Le Parisien reported that Dray had been the object of threats and attempted extortion in 2009. Investigators will reopen the files to see whether there is a link.
"At the moment it's impossible to say whether this was some kind of score settling or a burglary that went wrong," said the source.
Dray was born in Algeria in 1935 and launched his first company in the 1960s. He owned the famous Hôtel de Paris in the glitzy southern resort of Saint-Tropez and was in the process of renovating it for a grand opening in 2012. Dray also owned the National Hotel in Miami and the Pearl Hotel in Jerusalem as well as a chain of perfume stores.
Le Figaro spoke to some of the well-heeled residents of the neighbourhood where Dray lived.
"He was very discreet, as we all are round here," said one.
"You know, in this area, we don't see each other, we don't pass each other and it's fine like that," said another.