Last week's deadly fire - also in a building used by African immigrants - provoked street protests in Paris. Fourteen of the 17 who died in that blaze were children.
Members of the African community took to the streets over the weekend, urging the authorities to provide better housing for immigrants. They were joined by activists and pressure groups who accused French leaders of neglect.
The 29 August fire is the third deadly blaze to break out this year in a building used by African immigrants in Paris. A fire in a hotel killed 24 people in April.
Some 100 firefighters and 30 vehicles were used to control the latest fire, which is thought to have started in the lower part of the building. Fourteen people were injured, three of them seriously, fire officials said. The cause of the fire is not known.
Pierre Aidenbaum, the mayor of the third district, said some 12 families from the Ivory Coast had been living in the building.
"For years, people had been saying the living conditions there were dreadful," French news agency AFP quotes him as saying. He said the building's 40 residents were to have been relocated in September to allow for renovation work.