Graphene can develop large magnetic moments in custom-crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nanosystems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulenelike graphene systems and demonstrate that they possess a spin S=1 ground state. Scanning tunneling spectroscopy identifies the fingerprint of an underscreened S=1 Kondo state on these flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this S=1 π paramagnetism is robust and can be turned into an S=1/2 state by additional H atoms attached to the radical sites. Our results demonstrate that π paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behavior of interacting π spins in graphene systems.