The Future Circular Collider (FCC-hh) is a proposed successor of the Large Hadron Collider (LHC). FCC-hh would push both the energy and intensity frontiers of searches for new physics particles. In particular, due to higher energy and luminosity than at the LHC, at FCC-hh there would be produced around $\simeq\!30$ times larger amount of $B$ mesons and $\simeq 120$ times of $W$ bosons, which then may decay into feebly interacting particles. In this paper we demonstrate the potential of FCC-hh by studying its sensitivity to heavy neutral leptons (HNLs) with masses $m_{N} Journal version