The 44-year-old was hospitalised on Thursday after walking onto the playground of a high school in the southern city of Beziers with a jerry can of fuel and starting a blaze that left her with third-degree burns.
She staggered across the yard in front of her horrified students, some of whom joined teachers in rushing to her aid.
She was taken by helicopter to a specialist burns unit at the university teaching hospital in nearby Montpellier, but doctors could not save her.
"(The teacher) had third-degree burns over 95 percent of her body," a hospital source told AFP. "With these burns there was no way she could have survived."
Parents and pupils who spoke to AFP at the scene on Thursday said the teacher had a difficult relationship with several pupils in her maths class and that a meeting with them to clear the air on Wednesday had become rowdy.
On Friday morning, her colleagues staged a small protest outside the school in "solidarity" with their colleague, whom they identified as "Lise".
"Her gesture calls on all staff to show their solidarity and underlines the difficulty we have in carrying out our duties. We expect the authorities to act responsibly," the teachers said in a statement, brandishing signs reading "Never Again".
After news of her death emerged, one of the teachers, Christophe Quittet, said a silent march would be held in her memory departing on Monday afternoon from the school.
France's National Education Minister Luc Chatel expressed "deep sadness," in a statement issued as her death was announced, calling the episode "a distressing ordeal."
A psychological crisis cell was treating shocked students at the Jean Moulin secondary school, a sprawling establishment with more than 3,000 students and 280 teachers.
Top local education official Christian Philip said the school had reopened its doors on Friday morning for those seeking to talk about the tragedy but that all classes remained suspended until at least Monday.
Traumatised students were being assisted by a psychological crisis cell, he said, and about 80 students had already been treated. The cell was to stay in place until at least Tuesday.
In a joint statement, unions representing secondary school teachers said the incident underscored the hardships facing teachers and called for a public debate on working conditions.
Noting the "significance of the choice of the workplace to commit this desperate act," the unions called on Chatel to organise public consultations on "the realities" of teaching work.
"We must be aware of what is being called teachers' fatigue, professional problems, of the suffering at work that, while we see it in other professions, is more and more present within the education system," the unions said.
Local prosecutor Patrick Mathe said an initial investigation had found "no criminal act" connected with the incident.