The fire broke out in a building in Paris's 13th district at about 4 a.m. local time Wednesday, Radio France Internationale reported.
It took 93 firefighters with 30 fire trucks two hours to put out the flames.
Authorities said the fire started in the building's elevator shaft and damaged two apartments -- one on the sixth floor and one one the ninth.
Paris Mayor Betrand Delanoe offered condolences for the person who died and the three injured.
An investigation into the cause of the fire will be carried out, Delanoe said.