The man, now in his 60s, is being tried in Brig on charges of rape and sexual abuse for attacks that are believed to have started in 1996.
Many of his victims were younger than 16, according to the French edition of 20 Minuten daily.
The man is also accused of drugging and assaulting three girls in a dormitory at a private boarding school in Valais in 2000.
The report said the incident caused an uproar and the UK's Prince Andrew, Duke of York, withdrew his daughter from the school after the attacks occurred.
Other girls holidaying in Fiesch, Valais, were also drugged and assaulted in their sleep. The man was seized in 2007 in his home in Olten, after DNA testing on samples collected at the crime scenes proved his identity, the paper said.
He had already served prison term of 10 years in 1979 for repeated indecent assault on children and received psychiatric assistance.