“The person had been fighting for their life,” an official in the prosecutor’s office said.
The gunman, Cherif Chekatt, was killed in Strasbourg on Thursday night after firing on police, ending a two-day manhunt that involved more than 700 members of the security forces.
A fifth victim is brain dead. One of the victims has been identified as a Thai tourist, visiting Strasbourg with his wife as they wanted to avoid the Yellow Vests protests in Paris.
Eleven other people had been injured, four of whom were still in hospital on Friday morning, according to the Paris prosecutor.
Seven people were in police custody on Friday as part of the investigation into the attack.