The attack took place in a government building in Bourges, in the central Cher region, on Friday after Olivier Roson, a natural sciences teacher, became enraged after being refused a gun licence.
"He concedes the acts in question," said Vincent Bonnefoy, the public prosecutor in Bouges, reported local newspaper Le Berry Républicain. "He has not expressed any regrets."
The dead policewoman was named as Anne Pavageau, a mother of two children who had married in June. She grew up in Bourges and had been an officer in the town since 2006.
"I saw her every day," said a colleague. "She was always smiling, painstaking about her work and intelligent. Someone who was really well-liked."
Roson's attack was stopped after an officer shot him in the knee.
Interior minister Claude Guéant was quick to visit the scene on Friday where he said the drama should remind people the role of a police officer is "always dangerous."
Roson appeared in front of magistrates on Saturday and will face charges of voluntary manslaughter against the 30-year-old policewoman as well as charges of attempted murder of another policeman and a government official.