In the present paper, four fully biobased homopolyesters of 2,5-furandicarboxylic acid (2,5-FDCA) with a high molecular weight have been successfully synthesized by two-stage melt polycondensation, starting from the dimethyl ester of 2,5-FDCA and glycols of different lengths (the number of methylene groups ranged from 3 to 6). The synthesized polyesters have been first subjected to an accurate molecular characterization by NMR and gel-permeation chromatography. Afterward, the samples have been successfully processed into free-standing thin films (thickness comprised between 150 to 180 μm) by compression molding. Such films have been characterized from the structural (by wide-angle X-ray scattering and small-angle X-ray scattering), thermal (by differential scanning calorimetry and thermogravimetric analysis), mechanical (by tensile test), and gas barrier (by permeability measurements) point of view. The glycol subunit length was revealed to be the key parameter in determining the kind and fraction of ordered phases developed by the sample during compression molding and subsequent cooling. After storage at room temperature for one month, only the homopolymers containing the glycol subunit with an even number of -CH2- groups (poly(butylene 2,5-furanoate) (PBF) and poly(hexamethylene 2,5-furanoate) (PHF)) were able to develop a three-dimensional ordered crystalline phase in addition to the amorphous one, the other two appearing completely amorphous (poly(propylene 2,5-furanoate (PPF) and poly(pentamethylene 2,5-furanoate) (PPeF)). From X-ray scattering experiments using synchrotron radiation, it was possible to evidence a third phase characterized by a lower degree of order (one- or two-dimensional), called a mesophase, in all the samples under study, its fraction being strictly related to the glycol subunit length: PPeF was found to be the sample with the highest fraction of mesophase followed by PHF. Such a mesophase, together with the amorphous and the eventually present crystalline phase, significantly impacted the mechanical and barrier properties, these last being particularly outstanding for PPeF, the polyester with the highest fraction of mesophase among those synthesized in the present work.