After the body of a newborn was found in a thermal bag earlier yesterday, officers "discovered four more bodies of babies during their search" at the house in Louchats, near the city of Bordeaux, the source said, confirming a report by French television channel iTele.
The source added that the four corpses were found in a freezer.
The 40-year-old father was taken into custody while the 35-year-old mother was hospitalised, the source added.
The mother apparently "gave birth at home alone", the source said, adding that she had been taken to a hospital in Bordeaux "for gynaecological and psychiatric examinations".
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The woman "at this stage does not appear to have a history of mental illness".
The couple has two daughters aged 13 and 15.
The worst case of infanticide in recent French history dates back to 2010, when a mother admitted to killing eight of her babies, smothering them immediately after they were born.