I saw this one at the weekend – it’s another one where people know the difference between the two words but sometimes get into a pickle with phrases (see rein, rain or reign, peak, peek or pique, bear or bare or cue or queue for more examples of this issue).
So, fair means “just or appropriate” and “treating people equally” and “moderately good” as well as “blond(e)”, and the adverb fair means “in a fair manner”. So, “I said I will give all applicants fair treatment and judge them solely on their ability”; “Yes, the process was fair and everyone was treated appropriately”. “It’s not FAIR”, of course, too, when you expect to get something and you don’t. A fair is also a public entertainment made up of stalls and attractions, but I don’t think that is the version that gets confused.
Phrases associated with fair include fair and square (honestly and accurately); fair game (a reasonable target).
Fare, however, has a few disparate meanings, which is probably how the confusion creeps in. It refers to the money paid for a journey on public transport – “have you got change to pay the bus fare to get into town?”. It refers to a range of food – “traditional English fare is available at the pub”. And it is used in the sense of to perform in a specified way – “he fared badly in the local elections”. The archaic meaning of travel also survives in farewell (fare thee well, travel well).
So none of them are a fayre (that’s just a pseudo-archaic spelling of fair), and you fare badly, you don’t fair badly, which is the one I tend to see.