More than 70 firefighters rushed to the 20-unit building on Place Decelles around 6 a.m.
The fire started in a basement storage locker in the four-storey building and quickly spread to the main and second floors.
The fire forced residents out onto their balconies. Firefighters rescued them with ladders.
The only living being that was injured by the fire was a cat whose paws were burned. The cat was brought to safety by division fire chief Alain Chaussé himself.
The Red Cross sent buses to the scene to take care of those displaced by the fire.
It is not yet clear how badly the building was damaged.