The fire started late Saturday on the third floor of the building, forcing several people to jump out their windows in an attempt to escape the flames.
One person died after jumping out the window, another burnt to death on the third floor and a third died in hospital, officials said, adding that at least 13 people were injured.
A resident told journalists the blaze erupted when someone threw a petrol bomb during a brawl between occupants, but investigators could not immediately confirm the fire was criminal.
Housing Minister Cecile Duflot, who went to the scene, said authorities had not been aware of any "particular warning signs" at the 1920s-era building.
But Evelyne Yonnet, deputy mayor for housing in the suburb north of the French capital, said the building was "very badly managed" and had been inhabited by squatters.
"There had been complaints from residents," she told journalists.
Resident Ali Belmadi said the building, which housed around 60 people when it caught fire, had become "uninhabitable".
"The situation had been getting worse for five years," since squatters arrived, he told AFP.
"There were rats, cockroaches, no security," said another resident named Ghalia.