Three bodies were found soon after 8am in a seventh-floor flat near the Opera Garnier in the centre of the French capital. The blaze on the Boulevard des Italiens is believed to have started between 4am and 5am.
Those killed "couldn't get out of the window because of bars installed to prevent burglars getting in via the roof," said Ariel Weil, mayor of the city's four central districts.
"Around 10 people living on the same floor were rescued by firefighters who got in through the roof," he added.
Weil and a police source said investigators were looking into whether the fire could have started with a gas leak.
ANALYSIS Why do Paris apartment fires so often prove fatal?
Several firefighting vehicles were still on the scene by late morning, an AFP journalist saw, while central Paris prosecutors have opened an investigation.
Prosecutors are also probing a second deadly fire in the 15th district, near the Eiffel Tower in western Paris.
"A 60-year-old person was found dead and another is in critical condition, with two in serious condition," investigators said.
A second police source said a woman had been killed after the fire apparently broke out in her apartment.
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