  The future 100 TeV FCC-hh hadron collider will give access to rare but clean
final states which are out of reach of the HL-LHC. One such process is the $Zh$
production channel in the $(\nu\bar{\nu} / \ell^{+}\ell^{-})\gamma\gamma$ final
states. We study the sensitivity of this channel to the $\mathcal{O}_{\varphi
q}^{(1)}$, $\mathcal{O}_{\varphi q}^{(3)}$, $\mathcal{O}_{\varphi u}$, and
$\mathcal{O}_{\varphi d}$ SMEFT operators, which parametrize deviations of the
$W$ and $Z$ couplings to quarks, or, equivalently, anomalous trilinear gauge
couplings (aTGC). While our analysis shows that good sensitivity is only
achievable for $\mathcal{O}_{\varphi q}^{(3)}$, we demonstrate that binning in
the $Zh$ rapidity has the potential to improve the reach on
$\mathcal{O}_{\varphi q}^{(1)}$. Our estimated bounds are one order of
magnitude better than projections at HL-LHC and is better than global fits at
future lepton colliders. The sensitivity to $\mathcal{O}_{\varphi q}^{(3)}$ is
competitive with other channels that could probe the same operator at FCC-hh.
Therefore, combining the different diboson channels sizeably improves the bound
on $\mathcal{O}_{\varphi q}^{(3)}$, reaching a precision of $|\delta g_{1z}|
\lesssim 2 \times 10^{-4}$ on the deviations in the $ZWW$ interactions.
