Hold the phone, let's back up.
First, contact copying the roughly RGB screen of an Autochrome onto negative film would give you a reseau of CMY; not very good for separating color. Not to mention the unwanted density of the orange mask.
And, regardless, exposing through a screen onto color-negative paper would of course create a negative image on the paper. At the very best you would get a highly desaturated color negative on paper.
I do like the idea of getting a direct color print, but I'm afraid there's no easy way, and screen-plates are uniquely unsuitable for doing so. Afterall, the lack of any color is what makes white on a paper print, and a screen-plate by definition must have color all over its surface.