The schoolboy suspected of brutally stabbing to death a 15-year-old girl at their school in western France was a loner fascinated by Adolf Hitler, but had no clear motive for an attack which shocked the country, the prosecutor said on Friday.

The teenage boy killed the girl in a stabbing spree on Thursday at the private school in Nantes, inflicting 57 knife wounds to her body, mainly to the upper torso, skull and throat, according to prosecutor Antoine Leroy.

The attack prompted new soul-searching in France about teen violence and school security, with the prime minister suggesting metal detectors to prevent future attacks.

Investigators are working to determine the motive of the youth, who also wounded three other pupils in Thursday's attack at the Notre-Dame de Toutes-Aides high school.

The suspect, a teenager in the second year of high school, was arrested but then hospitalised on Thursday evening, rather than being placed in detention, after a psychiatric examination.

The teen is "extremely solitary," fascinated by Nazi leader Adolf Hitler and with "evidently suicidal" tendencies, said prosecutor Antoine Leroy, however adding that "no motive" could be put forward in a "certain manner" at this stage.

Witnesses said teachers overpowered the teenage student – whose identity has not been revealed, but who a fellow pupil also said had expressed an admiration for Adolf Hitler.

The suspect had sent a rambling email about "globalisation" to other students just before the attacks. (AFP)