The parents of a French schoolboy who killed himself after complaining of being bullied at school said they were disgusted by the response of the authorities, which included a threatening letter warning they could face prison for slander.

The 15-year-old boy, named as Nicolas, killed himself on September 5, one day after children went back to class in France after the summer break.

He had moved for the new term to an establishment in Paris, after complaining of being bullied during the previous school year at his former school in Poissy, in the Yvelines region southwest of the capital.

Rather than expressing sympathy with the family's predicament, the Yvelines regional education authorities, based in Versailles, sent them a letter saying statements made by the parents had been "unacceptable" and urged them to adopt a "constructive" attitude.

It even reminded them that slander in France can be a criminal offence punishable by up to five years in jail and a heavy fine of up to 45,000 euros ($48,000). The family had also received a dismissive letter from the management of the Poissy school.

"We were outraged and appalled to receive such letters," his mother Beatrice told AFP in a written exchange.

"Nicolas's father and I didn't understand it. We still don't understand it," she added.

The controversy has become a major embarrassment for the French government, which has sought to make combating bullying a top priority.

Education Minister Gabriel Attal said the threatening letter, which was sent in May but whose existence was first reported only last week by the BFMTV channel, was shameful.

Prime Minister Elisabeth Borne said it was "shocking".

The boy's mother said she was "relieved" by the ministers' comments, which she said acknowledged their son's suffering.

But she added the family would await the outcome of an investigation before deciding on any legal action.

Attal, 34, who this month had met the boy's family alongside first lady Brigitte Macron, is seen as one of the most ambitious ministers in President Emmanuel Macron's government.

He has made tackling bullying a priority after a series of high-profile suicides in recent years of children who had complained of being bullied at school.

Versailles prosecutors are seeking to investigate whether Nicolas's suicide was directly linked to bullying, cautioning against drawing any conclusions for now.

Attal is due on Monday to host a meeting of school regional authorities to discuss all the reports of bullying received over the last year.