Eugenics is a social philosophy that was popular in the US and Europe in the first half of the 20th century. The movement’s goal iswas to improve the quality of the human race by applying the same techniques used in animal and plant breeding to humans. Essentially, by encouraging the reproduction of humans with good traits, and discouraging the reproduction of humans with bad traits the good traits will become more prevalent over the bad traits. This movement quickly followed the popularization of Darwin’s evolutionary theory. Many countries, and some US states, introduced eugenics programs which involved the forced sterilization of people deemed unworthy to reproduce. The movement ended somewhat abruptly after World War 2 when the Nazi’s use of eugenic concepts in the Holocaust made the ideas unpopular.
Eugenics requires an understanding of biological inheritance that a theory of evolution provides It seems possible to me, that selectively breeding human populations for desired traits could become popular among the Medieval aristocracy. The royalty own the land and the serfs that lived on and work the land. Their descendants will own the same land and the descendants of those same serfs. It only seems natural that a land-owner would want to improve the quality of the serfs that work their land.
Another philosophy that emerged due to Darwin’s theories was Social Darwinism. Social Darwinists think natural selection is applicable to individuals in human society. They believe that inequalities in society are natural and are the result of superior individuals triumphing over inferior ones. Medieval societies were for the most part, extremely unequal. Concepts from Social Darwinism could be used as additional justifications for the existence of royalty and reinforce the idea that the king’s rightful place was at the throne while the peasants rightful place was in the hovel.
Of course these ideas are a product of their time, and wouldn't necessarily follow just from an understanding of human evolution, but I think these are potentially interesting for your world.