The mother, under hospital care, told investigators that she “wanted to put an end to her life and to take her children with her,” La République des Pyrenées reported on its website on Friday.
The woman remains under guard at the hospital, where despite her mental and physical condition, she was able to respond to questions from officers, the newspaper reported.
She faces charges for the murder of minors.
An autopsy on the bodies was to have been conducted on Friday.
The fire occurred on Wednesday night and was reported by the children’s father as he returned from work.
Fire fighters had little difficulty dousing the flames but the children were burned to a crisp, according to media reports.
The mother was discovered prostate in a state of “amazement”, Pau prosecutor Jean-Christophe Muller told reporters.
A knife was found nearby making it appear that she had initially intended to kill herself after killing her children, he said.
The husband, a state of shock so severe that he had to be hospitalized, said that his wife had suffered for several years from “personality problems”.