According to a reports in Le Figaro on Friday Dominique Leboucher, aged 55, the mayor of the village of Bretteville-le-Rabet in the department of Calvados was mortally wounded and castrated on Thursday night by a bitter love rival, who then committed suicide.
The killer had accused the mayor of having an affair with his partner, AFP sources claimed.
The attacker had no previous police record and was "clearly very much in love" with his girlfriend, Catherine Denis said.
He subsequently committed suicide.
Denis said the mayor's wife said she did not believe her husband was cheating.
The prosecutor said the mayor was apparently castrated after being murdered.
The crime sparked horror in the tiny village of Bretteville-le-Rabet in Calvados in northern France, but some questioned whether jealousy was to blame.
"I do not believe this thing about infidelity at all," said Yannick Guesnon, one of the mayor's deputies, adding that the attack appeared to be "an act of madness."
Albert Gibot, a pensioner in the village of 250 souls, said the attacker had "blown a fuse as his partner used to attend meetings of the local council in the evenings."
According to him, the councillor and the alleged murderer were not married but were the parents of two little girls.
The local gendarmerie has opened a murder investigation.
The commune of Bretteville-le Rabet stands around 15 km from the city of Caen and is home to around 250 residents.
The mayor, who worked in insurance sales first became a councillor in 2001, before taking up the post of deputy mayor in 2008. He was elected mayor in March's municipal elections.