The origins in America regarding April Fool's day are traced back to 1700 when the practice came with the advent of the first colonists which also called it "All Fool's Day."
The holiday became part of the traditions of France circa 1580 following of the mandates of the Council of Trent to switch the Julian calendar to the Gregorian. In the Julian calendar, the first week of the year would start in March 25 until April 1, but with the Gregorian it will start back in January 1.
With no phones, Internet, and with a rather slow moving of letters (especially among the lower classes) the news of the change came late to many, who kept on celebrating the week of March 25 to April 1 as usual. Those people were harrased and laughed at and played tricks upon.
Some researchers say that this was first the Roman celebration of Hilaria which involved costumes, and it took place during that first week of Spring taking place the last week of March and until the first day of April. The idea was that Nature "fools" people during that time by switching from cold to warm.