The French Le Point reports that the police think the shooter might be a neo-Nazi ex-soldier. However, since the only response to the previous shootings was an order for soldiers not to wear their uniforms outside their barracks, it seems that wasn't the line of investigation until now.
Via JPost:
The first murder linked to the gun took place on March 11. Police found the body of Imad Ibn-Ziaten, a 30-year-old staff sergeant of North African descent, dead behind a school in Toulouse. Investigators suspect the off duty serviceman was lured there by his murderer.
Last Thursday a gunman riding a scooter and wearing a black helmet opened fire on three French soldiers in uniform at a shopping mall in Montauban, a city 50 kilometers north of Toulouse. Abel Chennouf, 24, and Mohamed Legouad, 26, both of North African descent, were killed. Loic Liber, 28, of Afro-Caribbean descent, was left in a coma.(source)