The blaze in the French capital’s 16th arrondissement also slightly injured 27 people, including three firefighters.
The toll could still increase because the fire is still in progress on the seventh and eighth floors of the eight-storey block, a fire service spokesman told AFP at the scene.
Some of those affected scrambled on to nearby roofs to escape the smoke and flames, and needed to be rescued by fire crews.
About 200 firefighters were still at the scene in the early hours of Tuesday, battling the blaze and treating the injured.
The area is popular with tourists, with landmarks including the Trocadero overlooking the Eiffel Tower, Paris Saint-Germain’s home stadium the Parc des Princes, the Bois de Bologne and an array of upmarket shops and restaurants.
Fire service spokesman Clement Cognon said earlier: “We had to carry out many rescues, including some people who had taken refuge on the roofs.”
By about 3.30am, fire crews had finished evacuating the block on Erlanger Street but were still fighting the flames. Several surrounding buildings were also evacuated.
The cause of the fire is unknown.
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