Additive manufacturing (AM), particularly fused filament fabrication (FFF), has gained significant attention for its design flexibility and cost-effectiveness. This study focuses on optimizing FFF parameters that employ response surface methodology (RSM) to enhance the flexural performance of polyethylene terephthalate glycol (PETG) parts. Three essential parameters—layer height, print speed, and nozzle temperature—were varied, and their effects on flexural strength, flexural modulus, flexural toughness for ultimate strength, flexural toughness at 5% strain, and strain at ultimate strength were evaluated. Based on a Box–Behnken design, the experiments revealed significant effects of these parameters on the mechanical responses. The analysis of variance (ANOVA) indicates that layer height predominantly affects flexural modulus and toughness, while nozzle temperature significantly impacts flexural strength. The RSM models exhibited high accuracy, with R2 values exceeding 99%. Optimal parameter combinations yield remarkable improvements: flexural strength reached 39.55 MPa, flexural modulus peaked at 1344.60 MPa, flexural toughness for ultimate strength reached 218.22 J/mm3, flexural toughness at 5% strain reached 381.47 J/mm3, and strain at ultimate strength reached 3.50%. Validation experiments confirm the effectiveness of the optimization, with errors below 3.17%.