Firefighters are still searching for other victims and working to extinguish the blaze, according to spokesman Clement Cognon, of the city’s fire service.
He said the fire broke out early on Tuesday in an eight-storey apartment building on Rue Erlanger in the 16th arrondissement of western Paris.
The cause of the blaze is not yet known.
Mr Cognon said firefighters rescued two dozen people who had fled to the roof or climbed out of windows to escape the flames, and evacuated others from inside.
The building is less than a mile from the Roland Garros stadium that hosts the French Open tennis tournament, and close to the popular Bois de Boulogne park on the city’s western edge.
The 16th arrondissement is one of the most high-end districts of Paris.
More than 200 firefighters and emergency workers are on the scene, Paris police said, and the street is blocked off.
People in neighboring buildings were also evacuated.
The fire comes a month after a deadly explosion and blaze linked to a gas leak in a Paris bakery.