I’ve always (seemingly blindly) assumed it was April Fools Day, without a possessive apostrophe anywhere, thinking it meant it was April that verbally fooled people, or that the compound noun April Fools was acting adjectivally (as an attributive noun) to Day.
In short, I’ve always thought of it as (1) April Fools You Day, (2) April: Time for Practical Jokes Day, or (3) April: Time for Idiots Day, depending on the specific parsing.
Imagine my surprise, after being exposed to it for so long, to discover my mental myopia and unconscious personal editing of the grammar of the phrase. I’m just thankful I’ve never had occasion to style it incorrectly in any professional piece of writing or editing.
After looking into it a bit this year (I don’t know why this year is any different—aside from the particular circumstances in the world at the moment), I now know it’s most commonly styled as a day belonging to many fools in April: April Fools’ Day. In short, it’s April 1, the fools’ day.
Now, I’m curious to know if these people have always been fools, or if it’s a condition they are suddenly, and temporarily, afflicted with just once a year …