The suicide of a 13-year-old French boy who was bullied at school for being gay has shocked the country, prompting warnings that homophobia kills.

Prosecutors have opened an investigation into harassment of a minor after the boy, Lucas, hanged himself last weekend in the Vosges region of eastern France.

Regional prosecutor Frederic Nahon said late Thursday that the boy's friends told investigators he had been bullied "by pupils at his school for several months due to his homosexuality".

On Friday, Nahon added at a news conference that Lucas's journal contained an entry in which "he expressed his wish to take his own life".

Nahon said an ongoing investigation would determine whether there had been "a direct causal link" between the school bullying and the suicide, calling on police to proceed "with caution".

The probe also needed to verify the extent of any bullying, for how long it had gone on, and what exactly was said, the prosecutor said.

The investigation would also elucidate whether there had been any online harassment, he said.

The family has yet to file a criminal complaint, but the situation at the Louis Armand school in the town of Golbey has been reported to the education ministry, the prosecutor said.

"I am thinking of all the students like him who are bullied. Their despair is the basis of my determination to prevent all forms of bullying," France's Education Minister Pap Ndiaye wrote on Twitter.

Transport Minister Clement Beaune, who came out as gay while serving as Europe minister in 2020, tweeted: "Homophobia kills. Sadness and support to the family of Lucas."

"This is intolerable," added Diversity Minister Isabelle Rome. "All light must be shed on this tragedy and the homophobic circumstances surrounding it," she said.

Catherine Faivre, a lawyer representing the boy's family, told AFP that before considering filing a complaint the family "wanted to bury their son in peace".

The funeral is due to take place in the town of Epinal on Saturday. The Stop Homophobie anti-discrimination charity said his parents would ask mourners to bring LGBTQ signs in solidarity.

Faivre said there would be a solemn march organised in Lucas's memory in the coming weeks.

The local education authority said that Lucas had been the target of "mockery" at school since the end of the holidays in September.

"This was immediately taken seriously by the teams at the school, who showed great care on a daily basis," it said.

Nahon said, however, that there was no evidence of any recent inquest launched at Lucas's school into harassment allegations.