Sometimes referred to as All Fools' Day, 1st April is not a legal holiday, but its a good excuse for me to not turn up to work and is recognised internationally as a day for practical jokes and general nonsense.
In the Middle Ages, New Year's Day was celebrated on the 25th of March in most European towns. In some areas of France, New Year's was a week-long holiday ending on the 1st of April. The use of the 1st of January as New Year's Day was common in France by the mid-sixteenth century, and slick French city folk would play tricks on those backwater folk from the villages if they came to town on the 1st of April believing it to be new years day.
The traditional joke to play on someone in France, still practiced today in places, is poisson d'avril (meaning April's fish), which involves attempting to attach a paper fish to the victim's back without being noticed. This is also widespread in other nations, like Italy, where the term Pesce d'aprile (again meaning April's fish) is also used to refer to any jokes done during the day.
The whole fish thing is a reference to the abundance of newborn fish that were in French rivers at this time of year, and imply a person is as easy to fool as a newly hatched fish. And such frivolity it is to see your country neighbour go home with a fish stuck to his back.