You can book a ticket to Florence airport. Alternatively, when you take the train to Florence trainstation, you can take the tram to Florence airport - or take the train to Cortona.
Shuttle buses to Palazzone di Cortona will leave Florence airport on the 30th of June at 1530h. They will be in front of Arrivals and have the sign "CORTONA EVCM"
Shuttle buses from Palazzone di Cortona will leave for Florence airport on the 3rd of July at 1215h. Please book a return flight that does not leave before 1630h.