Two assailants were killed, including a woman who detonated a suicide bomb, a source close to the case said, adding that the police operation was continuing to flush out two other suspects.
The target of the raid, which filled the streets of Saint-Denis with heavily armed police and soldiers, was Islamic State militant Abdelhamid Abaaoud, who was initially thought to have orchestrated the Paris attacks from Syria, police and justice sources said.
A judicial source said police had originally been hunting other suspects in St Denis, but now believed he was one of those barricaded in the building.
Shooting began at about 4.30 a.m. (9 a.m. IST) and police special forces of the RAID unit were still involved in exchanges of fire three hours later, witnesses said.