According to Infoplease, it all depends what you mean by movie and colour, but they seem to include in their definition those Victorian slide shows which of course consisted of lots of still images shown in sequence. They moved but were they a movie? Probably not.
However, in 2012, someone discovered what is the earliest colour movie so far and like so many good things, it was made in England.

Made by Edward Raymond Turner, who had patented his colour process in 1899, the first colour moving pictures were found in an old tin at the National Media Museum. They date from 1902. There's a BBC clip
here.