The French authorities were searching on Monday for a man suspected in a string of methodical killings that have terrorized this city and the surrounding area in southwestern France, after an attack outside a Jewish school on Monday morning that killed four people, including three young children.

It was the third murderous attack on unarmed people in the region in little over a week, and the most deadly attack against Jews in France since a 1982 assault on a Paris kosher restaurant. The police said that the same gun, a .45-caliber automatic pistol, was used in all three shootings, the one Monday and two earlier attacks on French paratroopers, and that the modus operandi was the same — a man on a powerful motorbike, also the same in each instance, who shot and then fled. . .