  We study the two-photon production of the Higgs boson, $\rm \gamma\gamma\to
H$, at the Future Circular Collider (FCC) in ultraperipheral PbPb and pPb
collisions at $\sqrt{s_{NN}} = 39$ and 63 TeV. Signal and background events are
generated with MADGRAPH 5, including $\gamma$ fluxes from the proton and lead
ions in the equivalent photon approximation, yielding $\rm
\sigma(\gamma\gamma\to H)$ = 1.75 nb and 1.5 pb in PbPb and pPb collisions
respectively. We analyse the H$\,\to b\bar{b}$ decay channel including
realistic reconstruction efficiencies for the final-state $b$-jets, showered
and hadronized with PYTHIA 8, as well as appropriate selection criteria to
reduce the dominant exclusive $\gamma\gamma\to b\bar{b}$ continuum background.
Observation of $\rm PbPb\xrightarrow{\gamma\gamma}(Pb)\,H\,(Pb)$ is achievable
in the first year with the expected PbPb integrated luminosities.
