I found this story on Ludicrous Scene's blog here. The original source was The Sheffield Evening Telegraph, August 17, 1896.
"A Paris correspondent says a duel on bicycles was fought in the Boulevard Ney late on Saturday night.
"A large party of young fellows had been out cycling all day, and were returning home all very hilarious when two of them quarrelled, and decided to settle the dispute by duel with swords on their bicycles.
"The two combatants were placed 50 yards apart, and then ordered to charge. They rode at one another at a furious pace, but overshot the mark and failed to meet. Wheeling quickly round they returned to the charge, and this time came together with a terrific shock.
"Both were thrown, whilst the seconds who were following behind, also on bicycles, fell in their turn, and were both injured. Neither of the combatants touched the other with his sword, but in falling one ran his weapon into himself and his opponent injured his leg."