Analysis of the recovered ancient Neanderthal genome strongly suggests that they had very light pigmentation in hair, skin and eyes. Put simply, Neanderthals were white. Ancient DNA also suggests that the earliest modern humans in Europe, called Cro-Magnons, were dark pigmented relative to modern Europeans. Simply put, Cro-Magnons were "brown" (but did not have the modern sub-Saharan African phenotype, associated with the folk racial classification "black" in the United States, either).
The questions is whether light pigmentation in some modern humans in Eurasia arose from admixture with Neanderthals. The Neanderthal light pigmentation genes aren't identical to the modern European light pigmentation genes, but a new paper makes a tentative case that most of the light pigmentation genes in aboriginal Tawainese people, and to a much lesser extent in some other Eurasians (especially East Asians), could have a Neanderthal source.
I'm agnostic regarding how solid this evidence is at this time. Maybe the paper makes a really strong case for this, but I'm not convinced by what I have read summarizing the paper so far.