Investigators have yet to determine the cause, but France's presidency issued a statement saying the incident had "a criminal origin."
Nanterre prosecutors' office said the fire started around 3:30 am today in the suburb of Boulogne-Billancourt, west of Paris.
The Paris firefighters' press office said six people rescued with ladders were saved "from a certain death" and around a dozen people suffered minor injuries from inhaling toxic smoke. Nearly 300 people were evacuated and the fire was quickly extinguished.
Prime Minister Bernard Cazeneuve promised to investigate and expressed solidarity with the victims in a message posted on Twitter.