Bear with me here. King Richard had a court clerk by the name of Chauntecleer, a student of Roman history. He was particularly fond of the Roman festival of Hilaria which was celebrated on the eighth day after the vernal equinox. Geoffrey Chaucer mentions this celebration in his Canterbury Tales as being on the 32nd day of March.
Back to Richard. While Richard was not insane, he did have some particularly nasty character flaws, one of which was playing tricks on the peasants. Towards the end of one abnormally long peasant revolt in the winter of 1392, he declared that all of the peasant’s demands would be met and feeling satisfied, they all went home.
Eight days later, invoking the ancient feast of Hilaria, Richard rescinded his edict and declared the peasants to be fools and that the 32nd day of March would forever be known as April Fool’s Day in their honour.