The blaze, which started late on Monday, was the second deadly fire in a week at buildings housing immigrants in France's capital, and the third since April.
The three blazes, with a total of 48 victims, have focused attention on the plight of Paris's poor and their overcrowded lodgings.
In the latest fire, one of the victims was a six-year-old whose mother threw him out of a fifth-storey window to try to save him from the flames, police said.
The boy died at a hospital. The bodies of the mother, who was pregnant, and her three-year-old child were found in the burned-out wreckage.
On the same floor, firefighters found a second family in the charred building: a woman - pregnant with twins - her husband and their two children, police said.
Leaping from buildings
Two men were seriously injured by leaping from the building to escape the blaze, which ripped through a six-storey building in the 3rd Arrondissment of central Paris where Ivorian immigrants lived, firefighters said.
Eleven people, including five firefighters, had slight injuries.
About 130 firefighters battled
Days ago, a deadly blaze killed 17 Africans in Paris.
Four months earlier, 24 people died in a similar fire at a budget hotel that housed African immigrants.
French President Jacques Chirac urged investigators to work diligently and said the government would take "strong initiatives" soon to help families in inadequate housing.
"I want to stress how much this situation is unworthy of the natural requirements that we owe to people here in France, whatever their origin or nationality," he said on the sidelines of a meeting on French industry.
Interior Minister Nicolas Sarkozy ordered all havens for squatters - like the one that burned on Tuesday - shut down "because these are human beings housed in unacceptable conditions".
About 130 firefighters battled the blaze, which was believed to have started on the second floor of the building.
Police said they believed the fire was accidental. Residents had pirated electricity from a nearby building.
Gas cylinders and bedding on the ground fuelled the flames, police said.
"I want to stress how much this situation is unworthy of the natural requirements that we owe to people here in France, whatever their origin or nationality"
Forty to 60 people lived in the building, police said. Living conditions there were known by authorities to be "absolutely inadmissible and dangerous", said Pierre Aidenbaum, the district mayor.
Aidenbaum said the city intervened to have the rundown building bought six months ago and said he had started the process of searching for a place to relocate the families a month ago.
Deputy Paris Mayor Yves Contassot said the building was taken over by squatters after its owner abandoned it.
About half the families were illegal immigrants, he said.
A woman who lived in a nearby building, Elisabeth Sevre, said that the tenants were living in "frightening conditions" and that she often saw them taking water from a spigot on the street.
"We've known about this situation for four or five years," she said.
1000 unfit Paris buildings
Socialist Mayor Bertrand Delanoe said his team had counted 1000 unfit buildings in Paris when he became mayor in 2001.
"This situation has been around for decades," he said. "What we want is to attack this problem. We have been doing it for four and a half years."
Paris's mayor says there are
about 1000 unfit buildings
On Friday, 14 children and three adults were killed in a blaze in southeastern Paris at a dilapidated apartment building that housed African immigrants.
The fire drew angry calls for action on behalf of the needy.
French Interior Minister Nicolas Sarkozy pointed to overcrowding as a reason for the high death toll of that blaze and ordered an inventory of dangerous and cramped buildings.
Officials have ruled out an electrical short-circuit in that fire, and French police raised the possibility on Monday that the fire was caused by people, whether by accident or on purpose.