Fools, Fool's or Fools'?

If you do a quick google search, you'll see all three spellings. Which is the correct spelling?

- April Fools Day: the month of April has fooled day
- April Fool's Day: a day dedicated to one fool
- April Fools' Day: a day dedicated to multiple fools

There must be more than one fool in the world, so the correct spelling must be April Fools' Day, no?