The shooting occurred on Tuesday at around 16:30 p.m. local time in Roye Commune, Roye, about 110 kilometers (68 miles) north of Paris, in the Somme Department.
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French media Europe 1 said the child was just six months old, which was confirmed this evening by Cazeneuve.
Reports say a policeman was also among those killed and that two policemen were injured.
The gunman shot at the officers when they arrived, the AP said, leaving one critically injured and the other slightly wounded.
One of two police who were fired upon by the attacker died of his injuries.
Those injured have since been rushed by a helicopter to University Hospital of Amiens where they are receiving treatment. It took place on land occupied by travellers behind a police station.
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A police source told The Telegraph that the incident is understood to be “criminal matter”, and not linked to terrorism.
