Duoskelion structures have been recently introduced by Barchiesi et al. (2021) as a proof-of-concept motif for a new class of metamaterials. The properties of these periodic beam-like chiral structural elements have been investigated, up to now, by means of a discrete model formulation whose predictions are obtained by numerical methods. In this paper we select a specific scaling law for micro stiffnesses aimed at deriving, via asymptotic homogenization, an internally-constrained Cosserat one-dimensional planar continuum model as the limit of a duoskelion structure. We analyze qualitatively and quantitatively the family of equilibrium configurations of the homogenized continuum when subjected to axial loading and compare the results of the analysis with those obtained by means of the discrete model formulation.