French police are investigating whether a neo-Nazi gang was involved in the shooting attack Monday on a Jewish day school next to a synagogue in Toulouse.

Rabbi Jonathan Sandler of Kiryat Yovel, his two young sons and the young daughter of the school principal were gunned down by a man wearing a black helmet who had arrived at the school on a black motorbike. A 17-year-old boy was critically injured by the shooter, who reportedly chased children around the school.

The same two handguns used in the slaughter had also been used a week earlier in two similar shooting attacks on French paratroopers. Three were Muslim and all appeared to be either Middle Eastern or Black.

According to a report published in the French magazine Le Monde, police are now investigating whether a neo-Nazi gang was behind the murders. The magazine reported Monday that police have confirmed they are searching for three ex-paratroopers from Montauban who were dishonorably discharged from the army last year after being photographed in a Nazi salute in front of a Nazi flag, and wearing swastika tattoos.

The three were sacked from the same 17th Parachute Regiment as the victims who were shot last Thursday in Montauban, 31 miles (50 kilometers) away from Toulouse. A fourth soldier, a paratrooper from the 1st Parachute Regiment, had also been shot and killed the previous Sunday.

Investigators also confirmed Monday evening that they are investigating the connection between the murders of the soldiers and those at the Jewish day school.

Two Paris synagogues were sent threatening letters since Friday, one of which was received Monday morning. “You are the people of Satan, Hell is waiting for you,” was the message written in one of the letters, police sources told the AFP news agency. An investigation has been launched, but at last report, police had not yet linked the threats with the murders at the school in Toulouse.