The woman admitted being the mother of the children, suffocating them with a cushion, then wrapping their bodies in a plastic bag and placing them in the freezer, where they had spent up to a decade, prosecutor Laureline Peyrefitte said.
"First forensic investigations suggest, pending the results of an autopsy on the three babies and supplementary medical examinations, that the children were born alive," said Peyrefitte.
Based on the mother's testimony, she had given birth alone at her former home in the western city of Lorient in 1998, 1999 and again in 2003.
Each time she then "suffocated the newborns with a cushion before placing them in a plastic bag and putting them in the freezer," according to Peyrefitte, who later said the woman has been charged with murder and placed in detention. She could face a life jail term for the killings.
According to police investigations, a now-retired former work colleague of the unnamed woman fathered all three infants.
There have been several similar cases involving French citizens.
French authorities investigated after Courjault flew back to France where his wife and other children were on holiday.
Veronique Courjault, who also admitted to a third infanticide in 1999, received an eight-year jail term in 2009 but was released just months later.
In another case in March 2015, a 40-year-old man discovered the bodies of his partner's five infants in the southern village of Louchats.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)