To correctly answer this question, it should be noted that the fruits which are in the Fruits and Nuts season chart depend on different growing regions. For example: San Francisco and Oregon both are two separate places with different produce and harvest times. For the purpose of answering this question, we can take for example the Fruits Seasonality Chart of San Francisco. Here are a few of examples of fruits present in their season chart:
Almonds which are in season from August to November, apples which are in season from August to November, apricots which are in season from May to July, apriums which are in season from May to June, Asian pears from September to November, avocados from February to November, blackberries from May to October, and walnuts which are in season on October.