Fused filament fabrication (FFF) is one of the most widely used additive manufacturing processes and allows the production of complex parts. FFF can manufacture lightweight and strong structural components when processing high-performance carbon-fiber-reinforced thermoplastics. Although the process feasibility for printing 20% short-carbon-fiber reinforced PEEK was already demonstrated in the literature, a systematic study addressing the influence of printing parameters on different loading conditions is still lacking. Therefore, the present study investigates the influence of selected FFF parameters – i.e., layer height (LH), printing temperature (PT) and printing speed (PS) – on three mechanical properties: tensile (UTS), bending (UBS), and impact (UIS) ultimate strengths. The analyzed samples were printed and tested according to a central composite design of experiments, and each parameter's individual and combined effects were assessed by analysis of variance (ANOVA). Different regression models were obtained for each test, allowing the optimization of the parameters for each condition and resulting in three distinct optimized parameter sets. The relationship between parameters and microstructure was also assessed via fractography analyses, showing that lower LH and PS reduce the number and size of volumetric defects observed within the printed parts, as lower values improve interlayer cohesion. Contrarily, PT showed that average values (around 385 °C) benefit the microstructure the most, as higher temperatures result in larger defects and low temperatures reduce interlayer cohesion. Finally, the contour plots of the three produced models were overlaid to identify a universal parameter set capable of simultaneously correlating and maximizing all three performances. This procedure allowed the identification of the following optimized values: LH of 0.1 mm, PT of 385 °C and PS of 17.5 mm/s, resulting in the experimental UTS, UBS and UIS values of 116.7 ± 5 MPa, 167.2 ± 11 MPa and 28.2 ± 3 kJ/m2.