The sensitivity of the proposed FCC-ee collider to axion-like particles (ALPs) is investigated at all planned center-of-mass energies, with focus on the case where the ALP couples primarily to electroweak gauge bosons at leading order. We study the associated production of the ALP with a photon, with the ALP decaying in turn to two photons, yielding a three-photon final state. The ALP coupling to the photon is evaluated for ALP masses of 5 to 320 GeV. In this effective model, the FCC-ee will be able to detect ALPs for couplings down to a few 10^-6GeV^-1 (10^-5GeV^-1) during the Z pole run (WW, ZH, and tt̅ threshold runs). Additionally, this final state has the potential to probe the underlying electroweak structure of ALP couplings for ALP masses below the Z-boson mass.