The proposed hadron collider phase of the Future Circular Collider, FCC-hh, will record 30~$ab^{-1 }$ of proton-proton collisions at a center of mass energy of 85 TeV, providing an unprecedented dataset that extends both the energy and precision frontiers and enables high-statistics studies of rare processes, particularly within the Higgs sector.

With billions of single-Higgs events, the FCC-hh will measure rare decays such as $H \to \mu^+\mu^-$, $H \to \gamma\gamma$, and $H \to Z\gamma$ with percent-level precision and probe the top Yukawa interaction with unmatched accuracy through $t\bar{t}H$ production. The collection of tens of millions of Higgs-pair events will allow a few-percent-level determination of the Higgs self-coupling, a key parameter for understanding electroweak symmetry breaking and vacuum stability. Together with inputs from the FCC-ee, these measurements will test the Higgs sector with unparalleled accuracy.

This proceeding presents a selection of results submitted for the 2026 European Strategy for Particle Physics Update and provides an overview of the FCC-hh physics potential.