Celine Lesage, 38, a petite brunette with a teenaged son admitted to killing six of her babies between 1999 and 2007 before the judge in the Channel town of Coutances.
"I realise that I killed my babies, the children that I had with my two partners, but it's too difficult," she said during the hearing. "I want to understand but I can't," she said.
She told the court that she could explaim as to why she killed the baby.
Lesage, risked a jail sentencing which rules out the possibility of 18 years for first degree murder.
The accused was arrested in Oct 2007 following a complain from her partner and father of one of the murdered babies, after he found rotting infant bodies in garbage bags in the basement of their apartment building.
According investigators, Lesage appeared to be a shy woman, who showed no sign of mental illness. She claimed that she was scared of her ex-partner and father to five of the murdered babies, accusing him of violent behavior.
However, the court documents stated that the investigators did not find her ex-partner, 39-year-old plumber Pascal Catherine to be having a 'domineering attitude'.
Earlier, in June 2009, the court sentenced a Frenchwoman, Veronique Courjault to eight years pf imprisonment for killing three of her own babies. One of the corpses was burnt, while others were hidden in the family freezer.