The increase in luminosity and center of mass energy at the FCC-hh will open up new clean channels where BSM contributions are enhanced at high energy. In this paper we study one such channel, Wh → ℓνγγ. We estimate the sensitivity to the O⁽³⁾_φq, O_φW, and O_φW^~ SMEFT operators. We find that this channel will be competitive with fully leptonic WZ production in setting bounds on O⁽³⁾_φq. We also find that the double differential distribution in the p^h_T and the leptonic azimuthal angle can be exploited to enhance the sensitivity to O_φW^~. However, the bounds on O_φW and O_φW^~ we obtain in our analysis, though complementary and more direct, are not competitive with those coming from other measurements such as EDMs and inclusive Higgs measurements.