A man has been detained on suspicion of planning an attack on the Olympic torch relay in Bordeaux, French Interior Minister Gérald Darmanin has said.
He gave few details but praised police for ensuring security during Thursday's relay.
Prosecutors said the suspect had written a disturbing message that "could correspond to glorifying crime". He also referred to a previous mass killing in the US, they added.
The Olympic flame arrived in Marseille earlier this month, ahead of the Paris Games, which start on 26 July.
Paris 2024 organisers have spoken of an unprecedented security operation, with an opening ceremony involving more than 10,000 athletes being ferried along the River Seine.
The Olympic flame was due to arrive in Bordeaux late on Thursday afternoon, after a day of events marking its passage through the surrounding area.
Bordeaux prosecutor Frédérique Porterie said an investigation had been launched in response to an online message that referred to the killing of six people in their late teens and early 20s exactly 10 years ago in Isla Vista, California.
CNews said a post on the suspect's profile referred to Isla Vista killer Elliot Rodger, who had a deep loathing of women. His attacks inspired people online who identified as being " involuntarily celibate" - or incels.
The prosecutor said police then identified the suspect - named as Alex G - who was arrested on Tuesday. She said he had no criminal record but during a search of his home a rubber pellet revolver was seized along with several mobile phones and a computer.
"Initial investigations revealed the individual's interest in the Incel movement."
The suspect admitted in custody to "having considered an act with no specific location" in mind, and no mention of the Olympic flame relay.
He was also described as "psychologically highly fragile".
The Olympic flame is at the start of a 12,000km (7,500-mile) odyssey around mainland France and its overseas territories. Anti-drone experts have joined police in keeping a close eye on its journey.
The flame had been due to travel as far as the Pacific territory of New Caledonia, but rioting over the past 10 days has prompted organisers to cancel that leg of the route.
