Sinatra's affair with Princess Grace lasted for years, they even had a lovenest in a secluded French villa in Cap Ferrat

http://www.mirror.co.uk/news/uk-news/gra...

Yes they did, they both had a dark secret at the time and she was an sex-obsessed cheater. Her marriages to Prince Charming was not all that great.

As classy as he was, he probably had tons of affairs

Yes they sure did.