  We investigate the potential of the $pp\to \gamma\gamma\gamma$ process to
probe CP-conserving and CP-violating dimension-six operators of Higgs-gauge
boson interactions in a model-independent Standard Model effective field theory
framework at the center of mass energy of 100 TeV which is designed for the
Future Circular hadron-hadron Collider. Signal events assuming the existence of
anomalous Higgs boson couplings at $H\gamma\gamma$ and $HZ\gamma$ vertices and
the relevant SM background events are generated in MadGraph, then passed
through Pythia 8 for parton showering and Delphes to include detector effects.
After detailed examination of kinematic variables, we use the invariant mass
distribution of the two leading photons with optimized kinematic cuts to obtain
constraints on the Wilson coefficients of dimension-six operators. We report
that limits at 95\% confidence level on $\bar{c}_{\gamma}$ and
$\tilde{c}_{\gamma}$ couplings with an integrated luminosity of 10 ab$^{-1}$
are [-0.0051; 0.0038] and [-0.0043; 0.0043] without systematic error,
respectively.
