Turn of the century "dead seasons" would find the young French army private, and later secretary-general of the French Cycling Union, Daniel Gousseau cycling through the forests along side his horse-mounted general, sharing their love of the outdoors. He enjoyed these winter outings so much that he invited a few of his friends along and soon dozens of cyclists were rolling along the trails. Impromptu racing occurred among the sporting cyclists and soon organized events were scheduled.
In 1902 Gousseau was given the opportunity to organize the first French championship, which was won by F. de Baeder. For years this "rough stuff" and "mud plugging" remained mainly a French indulgence until its popularity exploded when Octave Lapize attributed his 1910 Tour de France win to the off-season sport. The first International Criterium, which was won by the Frenchman Gaston Degy, was held in 1924 in Paris. Following Gaston to the podium were many of cycling's greats: Charles Pelissier in 1926, 1927 and 1928, Sylvere Maes, the handlebar namesake, in 1933 and Robert Oubron who won in 1937, 1938, 1941 and 1942!
And from the always-plagiarizable Wikipedia:
Cyclo-cross began in the early 1900s as a way for European road cyclists to train during the winter months. Having to run whilst carrying their bike helped keep their feet and hands warm during the coldest part of the year. In addition riding off road in much more difficult conditions than smooth pavement increased the intensity at which the cyclists were riding. According to Konrad (1996) Daniel Gousseau of France is credited as having inspired the first cyclo-cross races and organizing the first French National Championship in 1902.