High molecular weight, fully biobased random copolymers of 2,5-furandicarboxylic acid (2,5-FDCA) containing different amounts of (1R, 3S)-(+)-Camphoric Acid (CA) have been successfully synthesized by two-stage melt polycondensation and compression molding in the form of films. The synthesized copolyesters have been first subjected to molecular characterization by nuclear magnetic resonance spectroscopy and gel-permeation chromatography. Afterward, the samples have been characterized from a thermal and structural point of view by means of differential scanning calorimetry, thermogravimetric analysis, and wide-angle X-ray scattering, respectively. Mechanical and barrier properties to oxygen and carbon dioxide were also tested. The results obtained revealed that chemical modification permitted a modulation of the abovementioned properties depending on the amount of camphoric co-units present in the copolymers. The outstanding functional properties promoted by camphor moieties addition could be associated with improved interchain interactions (π-π ring stacking and hydrogen bonds).