Forest Health and Biomass Energy Act of 2020 This bill addresses biomass energy, particularly with respect to materials removed from high-hazard areas (e.g., areas that pose wildfire risks). The bill directs the Department of Energy, in coordination with the Department of the Interior and the Department of Agriculture (USDA), to assess the potential to produce biomass energy from certain land under the administrative jurisdiction of Interior and USDA. With respect to the removal of timber located within certain high-hazard areas, USDA shall not charge a stumpage rate or assign any value to (1) certain trees, (2) forest processing residues or byproducts of forest restoration, or (3) a large dead tree that is not suitable for higher-valued wood products because of decay. The bill establishes the High Hazard Area Wood Biomass Fund, into which USDA may deposit a percentage of the revenue generated from base stumpage rates of timber sales that occur on National Forest System land to assist timber operators and biomass energy producers with the collection, harvest, storage, and transportation of biomass material removed from high-hazard areas. The President shall include in the annual budget submission an annual performance metric, which shall be established by USDA, for the harvest of wood biomass material in green tons made available for bioenergy markets.