Fiber-reinforced composites (FRCs) have emerged as a popular choice in the manufacturing industry due to their excellent mechanical properties and lightweight nature. Among the many classical composite manufacturing techniques like hand lay-up or filament winding process, the extrusion-based Additive Manufacturing (AM) has recently gained popularity owing to its high design flexibility, cost-effectiveness, and material efficiency. However, the existing design methodologies do not adequately consider the unique features of AM composites, limiting their potential. For example, conventional structural optimization methods focus only on the shape or topology of an FRC component, ignoring the crucial factor of fiber path orientation that imparts anisotropy to the component. Although popular density-based approaches like SIMP allow material orientation as an additional design variable, their solutions require additional post-processing tools or ad-hoc techniques to be manufacturable. To address these issues, this work proposes a new approach to optimize both the topology and fiber paths of FRCs while ensuring their manufacturability. A staggered scheme that combines two level-set methods is employed. An outer loop solves the Hamilton-Jacobi equation to optimize the topology for minimum compliance, while an inner loop employs nonlinear programming techniques to optimize the fiber paths by treating them as the level sets of a B-spline function. The key advantage in this approach is that the resulting solution is a set of curves that can be directly translated into printing instructions and printed without any additional processing. The proposed approach provides a significant step towards developing efficient design methodologies that leverage the unique features of AM to achieve optimal FRC performance.