It was widely reported about six months ago that European and some Asian peoples have up to 3% Neanderthal genes. Africans have none. I don't think anyone really challenged this data, so it is 'the best available science' that Europeans are part Neanderthal.
Larger brains equals higher IQ's. Neanderthals had larger brains than anyone alive today and presumably had a higher IQ too. Europeans and Asians have higher IQ's than Africans.