The children's father was said to have leapt from the building to raise the alarm
The blaze in Saint-Quentin, about 130km (80 miles) north-east of Paris, was probably accidental, reports say.
The children's father was present but escaped with serious burns, local officials said.
Three people were also killed and 13 hurt in a fire in the Paris suburb of Aubervilliers on Saturday. Officials suspect the fire was "of criminal origin" and an investigation has begun.
Officials said that the blaze in Saint-Quentin began at around 22:30 local time (21:30 GMT).
The father had been looking after the children for the first time since splitting up with his wife three months earlier, a neighbour told French media.
He tried to reach his children but was beaten back by the flames and jumped from the first floor of the building to raise the alarm, reports say.
Comment: The final word on Wikileaks is yet to be said, but knowing what we know about intel agencies and the way they operate, there has to be a high probability that either Wikileaks itself is compromised, or the information they are getting is, and there is no one smart enough there, including Assange, to figure it out. After all, ego very often blinds people to truth.