Nantes said in a statement overnight that the fan was "fatally injured" close to the club's stadium.
According to L'Equipe newspaper, the fan was a member of the Brigade Loire, Nantes' main group of passionate fans.
"In circumstances which are the subject of an ongoing judicial investigation, the 31-year-old collapsed, hit in the back," the club said. "Despite the intervention of emergency services, the fan could not be saved."
Nantes said the public prosecutor's office has launched an investigation into voluntary manslaughter.
"Witnesses interviews are underway and will continue throughout the night," the club added.
Quoting a statement from the prosecutor's office, L'Equipe said the Nantes fan collapsed after several vehicles carrying Nice supporters to the Beaujoire stadium were attacked by rival groups.