It's 1962. This is known thanks to the Hercules chasing scene (Founder's Day picnic) and also a major hint that is dropped at the beginning of the film. When Scott is moving in, the voice over states that it was the season that "Maury Wills would break the stolen bases record." Maury Wills stole a record 104 bases in 1962 and won the MVP with the Los Angeles Dodgers. That record stood until 1974.