This study investigates the mechanical properties of carbon and natural fiber-reinforced Polylactic Acid (PLA) and Polyethylene Terephthalate Glycol (PETG) composites produced via Additive Manufacturing (AM), focusing on Material Extrusion (MEX). The performance of filaments made from pre-consumer recycled PLA (rPLA) and PETG, with varying weight percentages of hemp and jute short fibers, was evaluated through tensile testing. Comparisons were made between the original filaments (PLA, carbon fiber-reinforced PLA [CF–PLA], and PETG) and their recycled versions. Multi-material compositions—neat PLA and PETG, single-graded (PLA + CF–PLA, PETG + CF–PETG), and multi-gradient (PLA + CF–PLA + PLA, PETG + CF–PETG + PETG)—were analyzed for mechanical properties. Optical microscope images of multi-material specimens were captured before and after fracture to assess failure mechanisms. The results indicate that the original CF–PETG filaments achieved a tensile strength of 50.14 MPa, which is higher than rPLA, PLA, and CF–PLA by 2%, 70%, and 6.7%, respectively. The re-manufactured PLA filaments reinforced with 7 wt% hemp fibers exhibited a tensile strength of 38.8 MPa, representing a 29% increase compared to the original PLA filaments and a 26% improvement over recycled PLA. Additionally, incorporating 7% jute fiber into PETG resulted in a tensile strength of 62.38 MPa, reflecting a 12% improvement over the original PETG filaments and a 15% increase compared to the recycled PETG filaments. Among specimens produced by AM, CF–PLA and rPLA demonstrated the highest tensile and compressive strengths. However, multi-material composites showed reduced mechanical performance compared to neat PLA and PETG, highlighting the need for improved interlayer adhesion. This study emphasizes the importance of optimizing material combinations and fiber reinforcement to enhance the mechanical properties of composites produced through AM.