Fused Filament Fabrication (FFF) can be significantly enhanced by integrating Continuous Filament Fabrication (CFF) embedding continuous carbon fiber reinforcements, enabling its application in load-bearing structures. However, the full potential of FFF is often constrained by existing design and manufacturing tools that fail to fully leverage the high design freedom inherent to this technology. In particular, conventional slicing software generates printing instructions based on predefined patterns, limiting the ability to optimize filament paths locally for enhanced structural performance. This computational work aims to develop tools for designing optimized filament paths to improve the structural performance of FFF parts combined with CFF. An algorithmic framework is introduced to derive in-plane filament paths for maximizing the stiffness or the strength of the printed component through the definition of a parametric surface having the print paths as its isolines. A specific objective is producing design solutions that are ready for manufacturing by incorporating manufacturing constraints with a specific focus on the minimum radius of curvature which is essential when working with continuous fiber-reinforced filaments. The mechanical performance of the solutions stemming from strength and stiffness optimization is critically compared for several case studies.