It is alleged the 73-year-old carried out the attack between 1998 and 1999. He was taken into custody for questioning last Tuesday by investigators.
AFP said the millionaire has been charged with the "rape of a minor by a person with authority over his victim". The news agency also maintains the complaint was lodged in 2017, citing the source.
Pippa Middleton married James Matthews last May at a wedding attended by Princes William and Harry.