Three French children died after they were found with their throats slit at their home near Paris on Friday, police said, adding that their absconding mother had been arrested in the capital.

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The doctor father of the children aged nine, 11 and 17 raised the alarm after returning home in the morning from work, police and judicial sources said.

"The children had their throats slit but we are still awaiting forensic reports," a judicial source said. The bodies of the nine-year-old girl and her 11-year-old brother showed multiple stab injuries.

The elder brother was found alive but later died of his injuries.

The killings took place in the suburban town of Dampmart, 30 kilometres east of Paris. The father was found in a state of shock and neighbours said he rushed out of his home screaming when he discovered the bodies.

A neighbour expressed shock, saying the family did not appear dysfunctional. "Everyone knew them here. It's unbelievable," said one, adding that the family was "discreet" and "had no problems."

However, investigators said the couple had been undergoing marital problems.