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 $( ubar{ u} / ell^{+}ell^{-})gammagamma$ 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.
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