April Fools' Day appears to have been around a long time. I've been reading a French magazine from 1924 which traces its origins back to a pagan tradition or even earlier. Presumably associating the day with trick and pranks dates from some common tradition but at some point the French separated out from many others when they adopted a fish as a symbol for the day, or rather for the fool, le Poisson d'Avril.
According to this particular article (and there are many different theories) the tradition dates back to the Hindu feast of Huli, celebrated in March to welcome spring. More recently, in France in 1564, Charles IX declared that the new year should start on 1 January rather than at Easter. Following this change people had to change their good wishes for a new year to a different time, but in the days when communications were poor, some continued to wish people well and give gifts on 1 April. Whether this was intended as a joke or whether the joke was on them, it became a tradition to mark a person as a fool by sticking a paper fish on his back. Why a fish? Probably because the day falls during the zodiac sign of the fish, Pisces.
Another tradition, one that I hadn't heard of before reading this article, is concerned with the last three days of March. These used to be called the "borrowed days". They are often very stormy (so much for March going out like a lamb!) and in years gone by people used think that March had borrowed the days from April in order to extend its reign. The very superstitious would neither lend nor borrow during these three days, not even the smallest object, because they were convinced that the borrower would use it against them like a charm.