  We take a bottom-up, first-principles approach to design a two-qubit gate
between fluxonium qubits for minimal error, speed, and control simplicity. Our
proposed architecture consists of two fluxoniums coupled via a linear
resonator. Using a linear coupler introduces the possibility of material
optimization for suppressing its loss, enables efficient driving of
state-selective transitions through its large charge zero point fluctuation,
reduces sensitivity to junction aging, and partially mitigates coherent
coupling to two-level systems. Crucially, a resonator-as-coupler approach also
suggests a clear path to increased connectivity between fluxonium qubits, by
reducing capacitive loading when the coupler has a high impedance. After
performing analytic and numeric analyses of the circuit Hamiltonian and gate
dynamics, we tune circuit parameters to destructively interfere sources of
coherent error, revealing an efficient, fourth-order scaling of coherent error
with gate duration. For component properties from the literature, we predict an
open-system average CZ gate infidelity of $1.86 \times 10^{-4}$ in 70ns.
