(1) Background: The paper addresses the effect of carbon fibers (CFs) treatment by low-temperature plasma with runaway electrons on the deformation behavior of the polyetheretherketone (PEEK)-layered composites. (2) Methods: The effect of the interlayer adhesion on the mechanical response of the composites was assessed through the tensile and three-point bending tests. In addition, computer simulations of the three-point bending were carried out with the use of the finite element analysis (FEM) with varying conditions at the “PEEK–CF layers” interface. (3) Results: DRE–plasma treatment during the optimal time of t = 15 min led to formation of a rougher surface and partial desizing of a finishing agent. The shear strength of the layered composites increased by 54%, while the tensile strength and the flexural modulus (at three-point bending) increased by 16% (up to 893 MPa) and by 10% (up to 93 GPa), respectively. (4) Conclusions: The results of the numerical experiments showed that the increase in the stiffness, on the one hand, gave rise to enlarging the flexural modulus; on the other hand, a nonlinear decrease in the strength may occur. For this reason, the intention to maximize the level of the interlayer stiffness can result in lowering the fracture toughness, for example, at manufacturing high-strength composites.