The woman has admitted that she is the mother of the dead child, who was found in a freezer in the town of Vichy.
Daily newspaper Le Parisien reported on Wednesday that the 15-year-old daughter of the woman went to a police station at the weekend to report the presence of the dead baby's body in the freezer.
When police caught up with the girl's mother, she confessed to giving birth to the child three years ago.
She claimed to have given birth in the bath of her home and said she had not realized she was pregnant.
Police doubt this is the case and the woman's daughter claimed her mother had "put on lots of weight."
The body found in the freezer measured between 62 and 64 centimetres, leading investigators to believe the child was between two and three months of age at the time of death.