The hydrogenation reaction of muconic acid, produced from biomass using fermentative processes, to bio-adipic acid is one of the most appealing green emerging chemical process. This reaction can be promoted by catalysts based on a metal belonging to the platinum group, and the use of a second metal can preserve and increase their activity. Pd–Au bimetallic nanoparticle samples supported on high-temperature, heat-treated carbon nanofibers were prepared using the sol immobilization method, changing the Pd–Au molar ratio. These catalysts were characterized by TEM, STEM, and XPS analysis and tested in a batch reactor pressurized with hydrogen, where muconic acid dissolved in water was converted to adipic acid. The synthesized Pd–Au bimetallic catalysts showed higher activity than monometallic Au and Pd material and better stability during the recycling tests. Moreover, the selectivity toward the mono-unsaturated changed by decreasing the Pd/Au molar ratio: the higher the amount of gold, the higher the selectivity toward the intermediates.