A family dispute drew police to the couple's home earlier in the day, when the wife told officers she planned to leave her husband.
The husband was “perfectly calm” and did not object to a neighbour driving his wife to the train station in the northern French town of Noyon, which is a short drive from their home, prosecutor Virginie Girard told reporters.
The wife left with three of the couple's five children, while two others stayed with neighbours.
But while the wife and the children waited on the train station platform, the husband appeared suddenly and opened fire. The wife and two children were killed.
The third child, a five-year-girl who is twins with one of slain children, was not wounded in the shooting.
“The attacker is an officer assigned to police headquarters in Paris who could not accept his spouse's intention to leave him,” Girard said.