A 35-year-old woman, who admitted giving birth to the babies between 1999 and 2006, and her boyfriend were held for questioning.
The boyfriend found the bodies after smelling rotting flesh and alerted the police last night. It was not immediately known whether the boyfriend was the father of any of the babies.
One of the bodies had a plastic bag on its head, in a sign the infant may have been suffocated after its birth.
The case is the third of its kind to make headlines in France in a year.
In August, police discovered the bodies of three babies hidden in boxes in a house in eastern France. The mother admitted she had tried to hide them, saying she kept them in various places, including a freezer, to avoid being discovered.
Both cases are reminiscent of the so-called "Seoul freezer babies" story, which made headlines in France last year.
Frenchwoman Veronique Courjault was taken into custody on suspicion of killing her two babies and storing their corpses in a freezer in the family's apartment in Seoul, South Korea.
Police sources have said Courjault also admitted to killing a third child.
Courjault, who has two other children, explained her actions by saying the pregnancies were unwanted. She could face life in prison if convicted of murdering her own children.