Wikipedia has various other possible explanations.
Sunday, April 01, 2007
It's April 1st and we are not going to play jokes. We looked in Chase's Calendar of Events, a reference book which comes out annually, and found quite a good explanation of how we got lumbered with a holiday on which it is ok to mislead and mock people... Chase's says, "April Fools' Day seems to have begun in France in 1564. April 1 used to be New Year's Day but the New Year was changed to Jan 1 that year. People who insisted on celebrating the "old" New Year became known as April fools and it became common to play jokes and tricks on them. The general concept of a feast of fools is, however, an ancient one. The Romans had such a day..."