At the ZH production optimum, around 240 GeV, the FCC-ee (CEPC) will be able to deliver 10 (5) ab-1 integrated luminosity in 5 (10) years with 4 (2) interaction points: hence to produce millions of Higgs bosons through the Higgsstrahlung process and vector boson fusion processes. This sample opens the possibility of sub-per-cent precision absolute measurements of the Higgs boson couplings to fermions and to gauge-bosons, and of the Higgs boson width. These precision measurements are potentially sensitive to multi-TeV range new physics interacting with the scalar sector. The ZH production mechanism also gives access to the invisible or exotic branching ratios down to the per mil level, and with a more limited precision to the triple Higgs coupling. For the FCC-ee, the luminosity expected at the top pair production threshold () further improves some of these accuracies significantly, and is sensitive to the Higgs boson coupling to the top quark.