In recent years, animal husbandry has aimed at improving the conditions of livestock animals useful for humans to solve environmental and health problems. The formulation of animal feeds or supplements based on antioxidant plant compounds is considered a valuable approach and an alternative for livestock productivity. Forest biomass materials are an underestimated source of polyphenolic compounds whose sustainable recovery could provide direct benefits to animals and, indirectly, human nutrition. In this context, an alcohol extract from leaves of Fagus sylvatica L. was first investigated through an untargeted ultra-high-performance liquid chromatography–high-resolution tandem mass spectrometry (UHPLC-HRMS/MS) approach. Then, it was fractionated into a fatty acid-rich and a polyphenolic fraction, as evidenced by total lipid, phenol, and flavonoid content assays, with antiradical and reducing activity positively correlated to the latter. When tested in vitro with rumen liquor to evaluate changes in the fermentative parameters, a significant detrimental effect was exerted by the lipid-rich fraction, whereas the flavonoid-rich one positively modulated the production of volatile fatty acids (i.e., acetate, butyrate, propionate, etc.).