The present study investigates the effects of fabrication parameters such as the nozzle temperature, the flow rate, and the layer thickness on the tensile strength of copper-filled metal-composite specimens. The selected material is a polylactic acid (PLA) filament filled with 65% copper powder. Two sets of 27 specimens each were fabricated, and equivalent tensile experiments were carried out using a universal testing machine. The experiments were planned according to the full factorial design, with three printing parameters, as well as three value levels for each parameter. The analysis revealed that the temperature and the flow rate had the greatest impact on the yielded tensile strength, with their contribution percentages being 42.41% and 22.16%, respectively. In addition, a regression model was developed based on the experimental data to predict the tensile strength of the 3D-printed copper-filled metal composite within the investigated range of parameters. The model was evaluated using statistical methods, highlighting its increased accuracy. Finally, an optimization study was carried out according to the principles of the desirability function. The optimal fabrication parameters were determined to maximize the tensile strength of the specimens: temperature equal to 220 °C, flow rate equal to 110%, and layer thickness close to 0.189 mm.