This work focuses on the manufacturing and characterization of highly environmentally friendly lightweight sandwich structures based on polylactide (PLA) honeycomb cores and PLA-flax fabric laminate skins or facings. PLA honeycombs were manufactured using PLA sheets with different thicknesses ranging from 50 to 500 μm. The PLA sheets were shaped into semi-hexagonal profiles by hot-compression molding. After this stage, the different semi-hexagonal sheets were bonded together to give hexagonal panels. The skins were manufactured by hot-compression molding by stacking two Biotex flax/PLA fabrics with 40 wt% PLA fibers. The combined use of temperature (200 °C), pressure, and time (2 min) allowed PLA fibers to melt, flow, and fully embed the flax fabrics, thus leading to thin composite laminates to be used as skins. Sandwich structures were finally obtained by bonding the PLA honeycomb core with the PLA-flax skins using an epoxy adhesive. A thin PLA nonwoven was previously attached to the external hexagonal PLA core, to promote mechanical interlock between the core and the skins. The influence of the honeycomb core thickness on the final flexural and compression properties was analyzed. The obtained results indicate that the core thickness has a great influence on the flexural properties, which increases with core thickness; nevertheless, as expected, the bonding between the PLA honeycomb core and the skins is critical. Excellent results have been obtained with 10 and 20 mm thickness honeycombs with a core shear of about 0.60 and facing bending stresses of 31–33 MPa, which can be considered as candidates for technical applications. The ultimate load to the sample weight ratio reached values of 141.5 N·g−1 for composites with 20 mm thick PLA honeycombs, which is comparable to other technical composite sandwich structures. The bonding between the core and the skins is critical as poor adhesion does not allow load transfer and, while the procedure showed in this research gives interesting results, new developments are necessary to obtain standard properties on sandwich structures.