The use of laser processing for the creation of diverse morphological patterns onto the surface of polymer scaffolds represents a method for overcoming bacterial biofilm formation and inducing enhanced cellular dynamics. We have investigated the influence of ultra-short laser parameters on 3D-printed poly-ε-caprolactone (PCL) and poly-ε-caprolactone/hydroxyapatite (PCL/HA) scaffolds with the aim of creating submicron geometrical features to improve the matrix biocompatibility properties. Specifically, the present research was focused on monitoring the effect of the laser fluence (F) and the number of applied pulses (N) on the morphological, chemical and mechanical properties of the scaffolds. SEM analysis revealed that the femtosecond laser treatment of the scaffolds led to the formation of two distinct surface geometrical patterns, microchannels and single microprotrusions, without triggering collateral damage to the surrounding zones. We found that the microchannel structures favor the hydrophilicity properties. As demonstrated by the computer tomography results, surface roughness of the modified zones increases compared to the non-modified surface, without influencing the mechanical stability of the 3D matrices. The X-ray diffraction analysis confirmed that the laser structuring of the matrices did not lead to a change in the semi-crystalline phase of the PCL. The combinations of two types of geometrical designs—wood pile and snowflake—with laser-induced morphologies in the form of channels and columns are considered for optimizing the conditions for establishing an ideal scaffold, namely, precise dimensional form, mechanical stability, improved cytocompatibility and antibacterial behavior.