We capitalize days of the week and months of the year, but when it comes to seasons, the rule is, we don’t. If we did, we would have to capitalize every particular time period, even those occurring throughout the day, like morning and afternoon. This would look absurd and get quite confusing.
Fall, being a season, is a general noun. Therefore, the capitalization that applies to proper nouns doesn’t apply to fall so the season fall is not generally capitalized.
There are situations, however, where fall is capitalized. For example, at the beginning of a sentence where the rule of the capitalizing the first letter applies. Other examples of when you can capitalize fall are when the season forms part of a proper noun, or when it’s a part of a title. For example in ‘Fall Games’ or ‘Fall Semester.’
Another example is when its personified in a piece of creative writing, like in poems. But this only applies when fall is given life in such writing.
Overall, the general rule is that we don’t capitalize seasons, fall included.