The older Mr. Matthews is a former racing driver who ventured into car sales and then hotels after a violent crash ended his racing career in 1973. In 1995, with his second wife, Jane, he bought Eden Rock on the Caribbean island of St. Barthélemy.
The French official said Mr. Matthews had been placed under judicial control but declined to comment further.
In France, complex criminal cases are handled by special magistrates with broad investigative powers, who place defendants under formal investigation when enough evidence of serious wrongdoing has been found. Magistrates can either drop cases they believe have insufficient evidence to go to court or summon defendants to stand trial.
The maximum sentence for rape in France is 15 years in prison, or up to 20 years if the victim was under 15.
President Emmanuel Macron has said that combating violence against women is one of the top priorities of his government.
The gender equality minister, Marlène Schiappa, recently put forward a draft bill, set to be debated by lawmakers in the next few months, that would among other measures declare that those aged under 15 could not legally consent to a sexual relationship.
It would also extend the statute of limitations in cases of sexual assault involving minors to 30 years, currently 20 years after the victim has turned 18.