The European forestry sector is a potential driver of transformation towards a sustainable bioeconomy. Forest products are increasingly used in high-tech and high-value-added industries, e.g., chemicals and the automotive industry. So far, however, research on the European bioeconomy has largely focused on agriculture as a provider of food, feed, fuel, and fiber to bio-based industries. Here we assess the potential impacts of a stronger reliance on forestry sector inputs to the European Union (EU28) bioeconomy on output, prices, final demand, and land use. Specifically, we run a sensitivity analysis of a 1% increase of input use of forest products in the EU28 economy in a Computable General Equilibrium (CGE) framework accounting for land use by Agro-Ecological Zones (AEZ) and greenhouse gas (GHG) emissions at high regional and sectoral resolution. We find that such a shift to a more forest-based bioeconomy would provoke small indirect land use effects globally due to existing international trade linkages and land market effects. Simulated increases in planted forest cover are associated with net GHG emission savings, but our scenario analysis also points to higher imports of forest products from countries with vulnerable tropical forest biomes, such as Brazil and Indonesia.