A police unit came across Cherif Chekatt in a Strasbourg street and shot him after he opened fire.
Three people have died following the shooting at the market and several more were seriously injured.
Chekatt, 29, had a string of criminal convictions in France and Germany and had become a radical Islamist in jail.
Interior Minister Christophe Castaner said three police officers had spotted a man matching Chekatt's description on rue du Lazaret, in the Neudorf area of Strasbourg at 21:00 local time (20:00 GMT).
