Cherif C., 29, has a lengthy criminal record with 27 offenses and has previously served jail time in France, Germany, and Switzerland.
French authorities have identified the suspect who remains on the run following a deadly shooting near a Christmas market in the city of Strasbourg.
Two people were killed while one person was left brain dead and a dozen others were injured after a shooting Tuesday, Paris public prosecutor Remy Heitz said at a news conference.
Police have deployed 350 officers to continue the manhunt Wednesday for "Cherif C.," Heitz said Wednesday. Cherif, 29, has a lengthy criminal record with 27 offenses and has previously served jail time in France, Germany, and Switzerland.
Four people close to the suspect have been detained but Cherif has yet to be caught.
Witnesses told police the suspect yelled "Allahu Akbar" (Arabic for "God is great") as he fired into the crowd.
The shooting took place shortly before 8 p.m. local time (2 p.m. ET) near a Christmas market that attracts millions of tourists every year. Strasbourg considers itself the "capital of Christmas."
Interior Minister Christophe Castaner had said the suspect exchanged shots with police after fleeing the scene late Tuesday.
Cherif got into a taxi and the driver later told officers he appeared to be injured, Heitz said.
Hours before, police had searched the suspect's home in a burglary probe and he was believed to have alleged criminal association with a terrorist group and attempted an assassination. Police uncovered weapons, including a grenade and four knives, Heitz said.
Strasbourg sits on the French border with Germany. On Wednesday, the German government it stepped up border controls in response to the attack, but will not be changing the security threat level for the country.