The growing demand for lightweight, high-strength, and high-stiffness materials has promoted significant research into the 3D printing of Continuous Fiber Reinforced Composites (CFRC). These manufacturing technologies enable the fabrication of complex geometries while retaining the mechanical properties of long continuous fibers, allowing the integration of advanced design tools such as topology optimization. The optimization of anisotropic materials such as CFRC, where the properties depend on the fiber orientation, has been extensively investigated; however, significant challenges remain. While existing methods successfully generate optimized topologies with optimum local fiber orientation, the resulting vector fields often exhibit discontinuities that make it difficult to interpret the intended fiber path. Consequently, these designs frequently fail to satisfy manufacturing constraints, such as minimum curvature and the prohibition of fiber overlapping. Furthermore, such discontinuities imply that the filament must be cut repeatedly during fabrication, a process that severely compromises the mechanical performance of CFRC. This work proposes a topology optimization framework tailored for long continuous fiber reinforcement. The strategy models each fiber as a Non-Uniform Rational B-Spline (NURBS) curve, which is mapped onto the analysis domain using a geometry projection approach. The method optimizes the NURBS curves, specifically the control point coordinates and their respective weights as design variables. Furthermore, to ensure manufacturability, a non-overlapping constraint is introduced, preventing fiber intersection within the printing plane. Numerical results demonstrate the method's capability to optimize structures using multiple fibers simultaneously. The generated designs satisfy the non-overlapping constraints while preserving the fiber path continuity, ensuring the manufacturability of optimized structures.