If you want a cheap flight from Jersey to Rome, you've got zero airlines to choose from.
Rome Leonardo da Vinci International (Fiumicino) Airport is just one of the airports in Rome. If you're not set on a specific airport, try changing your search from Rome Leonardo da Vinci International (Fiumicino) Airport to Rome to see a broader range of flights – they might be cheaper.
During this peak season, hotel and holiday prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.