Despite the advantages of polylactide (PLA), its inadequate UV-shielding and gas-barrier properties undermine its wide application as a flexible packaging film for perishable items. These issues are addressed in this work by investigating the properties of melt-mixed, fully bioderived blends of polylactide (PLA) and poly(ethylene furanoate) (PEF), as a function of the PEF weight fraction (1–30 wt %) and the amount of the commercial compatibilizer/chain extender Joncryl ADR 4468 (J, 0.25–1 phr). J mitigates the immiscibility of the two polymer phases by decreasing and homogenizing the PEF domain size; for the blend containing 10 wt % of PEF, the PEF domain size drops from 0.67 ± 0.46 µm of the uncompatibilized blend to 0.26 ± 0.14 with 1 phr of J. Moreover, the increase in the complex viscosity of PLA and PLA/PEF blends with the J content evidences the effectiveness of J as a chain extender. This dual positive contribution of J is reflected in the mechanical properties of PLA/PEF blends. Whereas the uncompatibilized blend with 10 wt % of PEF shows lower mechanical performance than neat PLA, all the compatibilized blends show higher tensile strength and strain at break, while retaining their high elastic moduli. The effects of PEF on the UV- and oxygen-barrier properties of PLA are also remarkable. Adding only 1 wt % of PEF makes the blend an excellent barrier for UV rays, with the transmittance at 320 nm dropping from 52.8% of neat PLA to 0.4% of the sample with 1 wt % PEF, while keeping good transparency in the visible region. PEF is also responsible for a sensible decrease in the oxygen transmission rate, which decreases from 189 cc/m2·day for neat PLA to 144 cc/m2·day with only 1 wt % of PEF. This work emphasizes the synergistic effects of PEF and J in enhancing the thermal, mechanical, UV-shielding, and gas-barrier properties of PLA, which results in bioderived blends that are very promising for packaging applications.