The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to interactions. Consequently, effective or interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.