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The design study of the Future Circular Colliders (FCC) in a 100-km ring in the Geneva area has started at CERN at the beginning of 2014, as an option for a post-LHC particle accelerators. The study has an emphasis on proton-proton and electron-positron high-energy frontier machines~\cite{FCCWebSite}. In the current plans, the first step of the FCC physics programme would exploit a high-luminosity of ${\rm e^+e^-}$ collider called FCC-ee, with centre-of-mass energies ranging from below the Z pole to the ${\rm t\bar t}$ threshold and beyond. A first look at the physics case of the FCC-ee can be found in Ref.~\cite{Bicer_2014}.  In this first look, the focus regarding top-quark physics was on precision measurements of the top-quark mass, width and Yukawa coupling through a scan of the ${\rm t\bar t}$ production threshold, with $\sqrt{s}$ comprised between~340 and~350\,GeV. The expected precision on the top-quark mass is in turn used used, together with the outstanding precisions on the Z peak observables and on the W mass,  in a global electroweak fit to set constraints on weakly-coupled new physics up to a scale of 100\,TeV. Although not alluded to in the first look, new physics might also show up via significant deviations of the top-quark electroweak couplings with respect to their standard-model predictions. Theories in which the top quark and the Higgs boson are composite lead to such deviations. The inclusion of a direct measurement of the ttZ coupling in the global electroweak fit is therefore likely to further constrain these theories. It is widely believed (as, e.g., in Ref.~\cite{Baer_2013}) that both a centre-of-mass energy well beyond the top-quark pair production threshold and a large longitudinal polarization of the incoming electron and positron beams are crucially needed to independently access the tt$\gamma$ and the ttZ couplings for both chirality states of the top quark. In Ref.~\cite{Baer_2013}, it is shown that the measurements of the total event rate, the forward-backward asymmetry, and the helicity asymmetry of the top quark with 500\,${\rm fb}^{-1}$ at $\sqrt{s}=500$\,GeV and with beam polarizations of ${\cal P} = \pm 0.8$, ${\cal P}^\prime = \mp 0.3$, allow for this distinction. The aforementioned claim is revisited in the present study. The sensitivity to the top-quark electroweak couplings is estimated here with an optimal-observable analysis of the lepton angular and energy distributions from ${\rm t\bar t}$ production in the $\ell \nu {\rm q \bar q b \bar b}$ final states (with $\ell = {\rm e}$ or $\mu$) at the FCC-ee, without incoming longitudinal beam polarization and with a centre-of-mass energy not significantly above the ${\rm t\bar t}$ production threshold.