I take a rather conservative view and say don't fast while doing Paragone or any parasite cleanse. It's also important to have clean bowels before you begin and to keep them moving during.
I myself chose not to do a parasite cleanse as none of my health issues really warranted so I'm not and expert about that - I just had candida due to taking too many Antibiotics , and all that entails, which does not really require a parasite cleanse. There are a ton of people who have done the parasite cleanse and they can help you over at the Parasite Cleanse forum. :)