A Greek Orthodox priest was shot and injured at a church in the French city of Lyon by an assailant who then fled.
The priest was fired on twice at around 4 p.m as he was closing the church, and was being treated on site for life-threatening injuries, the source said.
The incident came two days after a man shouting “Allahu Akbar!” (God is Greatest) beheaded a woman and killed two other people in a church in Nice, and two weeks after a schoolteacher in a Paris suburb was beheaded by an 18-year-old Chechen, apparently incensed by the teacher showing a cartoon of the Prophet Mohammad in class.
Ministers had warned that other Islamist militant attacks could take place.
President Emmanuel Macron has deployed thousands of soldiers to protect sites such as places of worship and schools.
Prime Minister Jean Castex, who was visiting Rouen, said he was heading back to Paris to assess the situation.
The Nice attack took place on the day Muslims celebrate the Prophet Mohammad’s birthday.
Many Muslims around the world have been angered about France’s defence of the right to publish cartoons depicting the Prophet.
A third person has been taken into police custody in connection with that attack, a police source said on Saturday. The suspected assailant was shot by police and remained in critical condition in hospital.