Biocomposites were prepared from a ternary matrix of polylactic acid (PLA), polycaprolactone (PCL), and thermoplastic starch (TPS) and reinforced with native fique fibers from southwestern Colombia. The influence of surface modification by alkalization of fique fibers on the interfacial properties of the biocomposite was studied using pull-out tests. Additionally, the effect of short fique fibers in three proportions (10%, 20%, and 30% (w/w)) on the tensile mechanical properties of the composite was evaluated. The experimental results indicated that the interfacial shear strength (IFSS) of the ternary matrix was predominantly influenced by PCL and characterized by the development of a weak interface that failed due to matrix yielding. Furthermore, the incorporation of short fique fibers increased the elastic modulus of the composite to values similar to those estimated with the Tsai–Pagano model. The alkalization treatment of the fique fibers improved the interface with the composite matrix, and this phenomenon was evidenced by the results of the micromechanical and tensile characterizations of the composite.