During the autumn in Puglia there's time for cachi or kaki in English, sometimes also called persimmon. This fruit is now quite popular in supermarkets throughout whole Europe, but on trees it can be seen only in the southern part.
Another worth noticing fruit is one the English call prickly pear and it can be found on opuntia (Opuntia ficus-indica to be precise). The fruit in Italy is usually called Fichi d'India.
Here you can see those fruits cut in halves.
In the autumn you can also find walnuts, in Poland called italian nuts but in Italy they are just only noce.