  We propose and demonstrate an architecture for fluxonium-fluxonium two-qubit
gates mediated by transmon couplers (FTF, for fluxonium-transmon-fluxonium).
Relative to architectures that exclusively rely on a direct coupling between
fluxonium qubits, FTF enables stronger couplings for gates using
non-computational states while simultaneously suppressing the static
controlled-phase entangling rate ($ZZ$) down to kHz levels, all without
requiring strict parameter matching. Here we implement FTF with a flux-tunable
transmon coupler and demonstrate a microwave-activated controlled-Z (CZ) gate
whose operation frequency can be tuned over a 2 GHz range, adding frequency
allocation freedom for FTF's in larger systems. Across this range,
state-of-the-art CZ gate fidelities were observed over many bias points and
reproduced across the two devices characterized in this work. After optimizing
both the operation frequency and the gate duration, we achieved peak CZ
fidelities in the 99.85-99.9\% range. Finally, we implemented model-free
reinforcement learning of the pulse parameters to boost the mean gate fidelity
up to $99.922\pm0.009\%$, averaged over roughly an hour between scheduled
training runs. Beyond the microwave-activated CZ gate we present here, FTF can
be applied to a variety of other fluxonium gate schemes to improve gate
fidelities and passively reduce unwanted $ZZ$ interactions.
