The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with approximately $50$-MHz frequencies and approximately $5$-GHz anharmonicities. The coupler enables the qubits to have a large tuning range of $XX$ coupling strengths (−$35$ to 75 MHz). The $ZZ$ coupling strength is < 3 kHz across the entire coupler bias range and < 100 Hz at the coupler off position. These qualities lead to fast high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a $\sqrt{iSWAP}$ gate in 258 ns with fidelity 99.72%, and by driving at the sum frequency of the two qubits, we achieve a $\sqrt{bSWAP}$ gate in 102 ns with fidelity 99.91%. This latter gate is only five qubit Larmor periods in length. We run cross-entropy benchmarking for over 20 consecutive hours and measure stable gate fidelities, with $\sqrt{bSWAP}$ drift ($2σ$) < $0.02%$ and $\sqrt{iSWAP}$ drift < $0.08%$.