The teen was carrying a rifle, two handguns and two grenades in the attack at the Alexis de Tocqueville high school in the sleepy hillside city of Grasse, police told AFP.
An interior ministry spokesman said eight people, including the principal, were injured. Some were hurt in a stampede triggered by the attack.
The suspect, who has not been named publicly, had shared pictures and videos on social media of infamous US school shootings, including the 1999 Columbine massacre.
The head teacher was admitted to the local hospital with gunshot wounds to the arm and three pupils were treated for buckshot injuries, the hospital's director Frederic Limouzy told AFP.
Investigators initially said they were looking for an accomplice but a police source later said the shooter, who was not previously known to the authorities, appeared to have acted alone.
Fifteen-year-old Mokhtaria told AFP she was having a cigarette in the school garage when she heard shots ring out.
France is still in a state of emergency after a series of terror attacks including the November 2015 massacre in Paris and a truck attack in Nice, just 40 kilometres from Grasse, in July last year.
The shooting comes just over a month before the first round of France's two-stage presidential election, in which security is one of the main issues on voters' minds.
All schools in Grasse were locked down after the late-morning shooting, which sent panicked pupils scurrying for cover.
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