Proteins adsorbed onto biomaterial surfaces facilitate cell-material interactions, including adhesion and migration. Of particular importance are provisional matrix components, fibrinogen (Fg) and fibronectin (Fn), which play an important role in the wound healing process. Here, to assess the potential of a series of elastomeric poly(butylene succinate) copolymers for soft tissue engineering and regenerative medicine applications, we examined the adsorption of Fg and Fn. We prepared spin-coated thin films of poly(butylene succinate) homopolymer and a series of elastomeric poly(butylene succinate) copolymers with butylene succinate (PBS, hard segment) to succinate-dimer linoleic diol units (DLS, soft segments) weight ratios of 70:30, 60:40, and 50:50. X-ray diffraction was used to assess crystallinity, while the obtained thin films were characterized using quartz crystal microbalance with dissipation monitoring (QCM-D) and atomic force microscopy (AFM). Protein adsorption was assessed using QCM-D, followed by data analysis using viscoelastic modeling. On all three copolymers, we observed robust adsorption of both key provisional matrix proteins. Importantly, for both proteins, viscoelastic modeling determined that the adlayers were 30–40 nm thick and had low shear modulus values (<25 kPa), thus indicating soft orientations (end-on for Fg) or conformations (open for Fn) of the hydrated proteins. Overall, our results are very encouraging, as they predict excellent cell adhesion and migration, key features enabling tissue integration of potential PBS-DLS scaffolds.