Fowl refers to birds, especially chickens and game birds. It has no non-bird-related definitions. Foul has many definitions, including (1) offensive to the senses, (2) morally detestable, (3) a violation of rules of play, (4) to make dirty, and (5) to commit a violation against rules of play.
Foul is the correct spelling in the phrasal verb foul up (meaning mess up) and in the phrases foul play (meaning illegal activity); foul-mouthed (meaning tending to use offensive language); no harm, no foul (meaning no serious damage done); and cry foul (meaning to accuse someone of unfair practices or wrongdoing).
Fowl is occasionally used in place of foul, especially, for mysterious reasons, in the phrase cry foul—for example:
Gwyneth gets steamed! Star cries fowl over Times accusation that she used a cookbook ghostwriter [New York Daily News]
But the latter two have cried fowl, claiming Tolly refused to test products they say would have yielded different results. [TechNewsWorld]
Counties cry fowl over FL Medicaid legislation [WTXL.com]
The opposite error occurs as well, though examples such as this one are harder to find:
She gets as excited over the water foul as a puppy, barking at the geese, ducks and swans as if they would actually come play with her. [Livingston Daily]
When the subject involves birds, many writers can’t resist the bad pun, especially in titles—for example:
Crying fowl over tower plans [Reading Eagle]
Fowl discovery: Woman discovers white feather in the middle of her chicken nugget [Daily Mail]
Fowl play suspected in theft of giant chicken [Hamilton Spectator]