Apparently the motive is racism as declared by Sarkozy.
"French President Nicolas Sarkozy said that the same gunman who shot dead a teacher and three children at a Jewish school in Toulouse on Monday was also responsible for the killing of three soldiers last week, apparently motivated by racism. French paper Le Point reported that French police are searching for three former paratroopers in connection with the Toulouse Jewish school shooting that left four dead. French police said earlier Monday that forensic evidence revealed the gun used to kill four people -- a teacher, his two children and another child -- at the Ozar Hatorah school was the same used to slay three French soldiers on two separate occasions nearby."
Sarkozy: Racism behind Fren... JPost - Jewish World - Jewish News
8-year-old Miriam Monsonego, daughter of school headmaster Rabbi Yaacov Monsonego, who was killed in a shooting attack at the Ozar Hatorah School in Toulouse, France
There were reports in France that police were looking for three former soldiers of the logistics regiment sacked for "neo-Nazi" activities. The men were all ejected from the army in 2008 after a photograph emerged of them making Nazi salutes in front of a swastika. "Police are interested in locating those men to see if there may be some connection," said a source close to the investigation.
Toulouse shooting: little girl cornered in school and shot in head - Telegraph
'There's a monster on the loose': Sarkozy's warning as police reveal Toulouse serial killer could have filmed horrific murders.
Criminologist: Toulouse Killer Is Local Man
Toulouse Killer Is Local Man Who Knows Area Well, Says Criminologist Professor David Wilson | World News | Sky News