Police say a 24-year-old computer science student was arrested after officers found a large number of weapons in his car.
It's believed the man was known to security services and wanted to travel to Syria.
Interior minister Bernard Cazeneuve told reporters the man is also being questioned on suspicion killing a young woman.
He was detained on Sunday after apparently shooting himself by accident and calling an ambulance.
When detectives arrived at the scene it's claimed they found a note with a list of potential targets including a number of churches.
Premier understands the suspect is Algerian and had been living in South East Paris.
Police said there was no immediate indication the man had ties to any Islamic extremist group.
Christian security analyst Simon Barrett told Premier's News Hour it was a worrying development.
He said: "I think this is very disturbing and clearly what it shows is that there is an escalation in the terror threat that France is currently facing, it was only in January that the world was shocked by the Charlie Hebdo attack,
"Now we're seeing churches and the Christian community attacked and I think it's time that Christians in the West woke up to this new reality of Christians facing persecution in the Middle East and now coming home here in Europe."
Simon Barrett speaking to Premier's Hannah Tooley: