A further 27 people were being treated for minor injuries, mostly due to smoke inhalation, after the blaze began about 5am on Nemours Street, in Paris’s 11th district.
Local authorities, including Paris' police commissioner, are still trying to determine the cause of the blaze, which it is thought may have begun in the stairwell of the six-storey building before spreading to two neighbouring buildings.
A spokesperson for the fire brigade said a young woman died after jumping out of the window, while the bodies of two other people were found in their apartment. The seriously injured person was rushed to hospital in a critical condition.
Some 200 firefighters attended the scene, and by 9am the fire was under control but not extinguished.
Local district mayor François Vauglin said that to his knowledge the building, which also housed a restaurant and a Hamman, did not have any structural problems.
Meanwhile Anne Hidalgo, the mayor of Paris, tweeted : “All my thoughts go this morning to the families and loved ones of the three Parisians who died in the fire on rue de Nemours, in the 11th arrondissement. Paris is in mourning.”
The Paris prosecutor's office has opened an investigation.