The armed 17-year-old was arrested after the shooting, which happened at the Alexis de Tocqueville school in the town of Grasse, about 40 kilometres from the southern city of Nice.
France's Government sent out a mobile phone app alert warning of a possible terrorist attack after police initially reported that shots had been fired.
But authorities have since said they believe there is no reason to suspect the attack was terror related.
A police official said in addition to the three wounded in the shooting, five other people were being treated for shock. None of the injuries were life-threatening.
The official, who was not authorised to be publicly named, said there did not appear to be any other suspects, but police were working to "remove all doubt".
Police cordoned off the area and worried residents gathered outside, along with several emergency vehicles.
An employee of a nearby electronics store, who would not provide his name, said police had asked residents to stay indoors.
The Government's alert warning came via a system implemented after the deadly November 2015 attacks in Paris.
The incident provoked shock around the country, where school shootings are rare.
France remains tense and under a state of emergency after several deadly Islamic extremist attacks over the past two years.