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The Future Circular Collider project at CERN constitutes a global European strategy for particle physics in the next 50 years. It is based on the construction of a 100 km tunnel in the Geneva area that would first accommodate an electron-positron collider (FCC-ee) to measure precisely the properties of the Z, W, and H bosons, and of the top quark. This collider would later be replaced by a 100 TeV pp collider (FCC-hh), to push the energy frontier established by the LHC. Prospects for Higgs physics at these facilities will be presented, with an emphasis on the unprecedented level of precision provided by FCC-ee for Higgs couplings, including the Higgs self coupling.