The suspect was wounded in the chest during the June 6 attack. He had allegedly attacked officers on duty at the headquarters.
Tourists ran from the attack, BBC News reports. The attack closed the area around the historic cathedral, and people were asked to stay away.
The incident follows a London attack in which Islamic extremists used a van and knives to kill seven and wound dozens of people.
Extremist attacks in Paris in 2015 killed 147.
France has experienced several terrorist attacks in recent years, including a July 2016 attack in Saint-Etienne-du-Rouvray in which a priest was murdered while saying Mass.