Firefighters in Pau cleared 30 residents from the four-storey building early on Tuesday morning.
They were called at 6.40am by a resident "who could not open the door of the apartment where the fire occurred and who was concerned because they saw blood running down the edge of one of the apartment's windows", a member of the emergency services told the AFP news agency.
They found the bodies of five people inside the first-floor apartment and a couch on fire.
Apart from the child, the dead were two couples.
One of the women had been bound and gagged, with adhesive tape around her neck.
Evidence of violence was found on the other couple but not on the child, who appears to have died from the effects of the fire, the sources say.
Neighbours say that three out of the four adults were of Spanish origin and that the child was two years old.
"There seems to have been a domestic incident that turned into a massacre," Pau deputy mayor Jean-Paul Brin told AFP.