Biopolymers are gaining increasing importance as substitutes for plastics derived from fossil fuels, especially for packaging applications. In particular, furanoate-based polyesters appear as the most credible alternative due to their intriguing physic/mechanical and gas barrier properties. In this study, block copolyesters containing 2,5-furan and trans-1,4-cyclohexane moieties were synthesized by reactive blending, starting from the two parent homopolymers: poly(propylene furanoate) (PPF) and poly(propylene cyclohexanedicarboxylate) (PPCE). The whole range of molecular architectures, from long block to random copolymer with a fixed molar composition (1:1 of the two repeating units) was considered. Molecular, thermal, tensile, and gas barrier properties of the prepared materials were investigated and correlated to the copolymer structure. A strict dependence of the functional properties on the copolymers’ block length was found. In particular, short block copolymers, thanks to the introduction of more flexible cyclohexane-containing co-units, displayed high elongation at break and low elastic modulus, thus overcoming PPF’s intrinsic rigidity. Furthermore, the exceptionally low gas permeabilities of PPF were further improved due to the concomitant action of the two rings, both capable of acting as mesogenic groups in the presence of flexible aliphatic units, and thus responsible for the formation of 1D/2D ordered domains, which in turn impart outstanding barrier properties.