A primary school teacher in the southern French town of Albi has been stabbed to death in front of her class by a pupil's mother, police say.
Fabienne Terral-Calmes, 34, was attacked at the Edouard Herriot school on Friday morning.
The suspect, 47, was arrested at home shortly afterwards, prosecutors say.
Education Minister Benoit Hamon said she appeared to have a "serious psychiatric disorder", according to initial investigations.
Sending the minister to the scene, President Francois Hollande pledged that all the services of the state would be "mobilised to take care of these children and the staff who witnessed this awful tragedy".
The attack came on the last school day before the summer break, when Ms Terral-Calmes was teaching her class, believed to be aged five to six. She herself was the mother of two young children.
The attacker was bringing her own daughter, aged five or six, to school as usual on Friday when she produced a long knife, French broadcaster France Info reports.
She is said to have shouted "I am not a thief" before attacking.
Ms Terral-Calmes was stabbed just once, either in the chest or stomach, according to different reports.
Albi prosecutor Claude Derens was one of the first at the scene.
"When I arrived at the scene they were trying to revive her," he said. "She was in cardiac arrest in her classroom."
Local media reported that the suspect was already known to police over allegations of child neglect.
France's Le Point magazine reports that the suspect, who was not named officially, later told police her act was justified because "the teacher was bad" to her daughter.
But a representative of school parent groups in the region said there had been no particular problems between the teacher and her attacker, who is believed to have had her daughter in the school for just six weeks.
Analysis: Hugh Schofield, BBC News, Paris
Fatal attacks on teachers are of course extremely rare. But there is nonetheless a context to this ghastly event - and that context is the growing problem of violence in French schools.
Some of that violence is student on student; some of it is student on teacher; but there is also a worrying increase in outbursts of hostility from parents on teachers, especially in junior schools.
An official report earlier this year found that almost half of school heads in elementary schools and kindergartens had faced verbal attacks from parents. A small minority of these have also faced physical assault.
The most common pretext for the abuse is that a punishment meted out on a child is unjust. According to the report's author, teachers are getting so anxious that they are shutting themselves off from contact with parents - which only increases the level of mistrust and creates the conditions for more hostility.
The pupils who witnessed the attack are receiving counselling.
A spokesman for the education minister said that he was "deeply shocked by this crime, which plunges the end of the school year into mourning".
"This tragedy confirms there is a need to fight against violence in and around schools, to protect schools, teachers and students," the spokesman said.
More than one in 10 teaching staff in France's public education system has reported suffering abuse or threats at work - nearly twice as many as in all other professions, according to a recent study by the French national statistics institute.