The 35-year-old suspect shouted "Allahu Akbar" - Arabic for "God is greatest" - when arrested by police, local prosecutor Arnaud Laraize told Sud Ouest newspaper.
French media said the motive for the attack remained unclear and that the anti-terrorism prosecutor's office was not in charge of the inquiry at this stage.
The prosecutor's office could not immediately be reached for comment.
At least nine people were injured when the suspect's car hit them in various areas of Oleron island, the mayor of Dolus-d'Oleron, Thibault Brechkoff, told BFM TV.
Nunez said two of the injured were in intensive care - some French media later said that was the case for four of them.
Le Parisien newspaper said investigators were looking into the possibility that the suspect might be mentally disturbed.
The man was previously known to police for petty crime including driving while drunk as well as drug-related offences, local newspaper Charente Libre and other French media reported, citing the mayor of Saint-Pierre d'Oleron, Christophe Sueur.
"He is known for minor offences such as theft," Sud Ouest newspaper quoted Laraize, the prosecutor, as saying.
"He was not on the S watchlist," he said, referring to an investigators' list of radicalised individuals.
Charente Libre newspaper said the suspect is French, without citing sources.
The suspect also tried to set fire to his car, which contained one or several gas canisters, French media reported.
