Two experts in early film technologies had to create a special gate to hold the film's frames, and then match the differently colored frames individually before capturing the image digitally, restoring it, and combining it into a motion picture. Going into the project, it wasn't clear whether the process would work.
"Then we saw it on screen. We looked at it and we were absolutely astonished with it. We never expected it to be so good... Knowing all about colour reproduction, and all the pitfalls along the way, to do something as good as that coming from 1901, 1902 was really totally unexpected. It was very exciting."
While a number of early filmmakers produced "color" movies, those were produced by adding color to individual frames of the normal black&white film stock. Capturing natural color on single film stock didn't make inroads into the film industry until the late 1920s and early 1930s.
Source - World's first colour film footage viewed for first time, BBC News
edit - had to correct a couple of technical steps in the restoration process.