PARIS — A millionaire British hotel owner who is the father-in-law of Pippa Middleton, the sister of the Duchess of Cambridge, is under formal investigation in France over allegations that he raped an underage girl in the 1990s, a French judicial official said.

The businessman, David Matthews, an owner of the luxury resort Eden Rock, faces potential charges of “rape on a minor by a person with authority over the victim” for events said to have taken place in 1998 and 1999 and for which a complaint was filed last year, according to the official.

Mr. Matthews, 74, was questioned in Paris on Tuesday by police officers who specialize in crimes involving minors, said the official, who spoke on the condition of anonymity in line with departmental policy. No further information was immediately released.

A spokesman for Mr. Matthews told the newspaper The Telegraph that he “categorically denies the allegation and unequivocally contests the untrue and scandalous accusation.”