A more environmentally friendly method for creating sustainable alternatives to traditional aromatic–aliphatic polyesters is a valuable step towards resource-efficiency optimization. A library of furan-based block copolymers was synthesized via temperature-varied two-step polycondensation reaction in diphenyl ether using Candida antarctica lipase B (CAL-B) as a biocatalyst where dimethyl 2,5-furandicarboxylate (DMFDCA), α,ω-aliphatic linear diols (α,ω-ALD), and bio-based dilinoleic diol (DLD) were used as the starting materials. Nuclear magnetic spectroscopy (¹H and ¹³C NMR), Fourier transform spectroscopy (FTIR) and size exclusion chromatography (SEC) were used to analyze the resulting copolymers. Additionally, crystallization behavior and thermal properties were studied using X-ray diffraction (XRD), digital holographic microscopy (DHM), and differential scanning microscopy (DSC). Finally, oxygen transmission rates (OTR) and dynamic mechanical analysis (DMTA) of furan-based copolyesters indicated their potential for medical packaging.