Swimming in nature achieves remarkable performance through diverse morphological adaptations and intricate solid-fluid interaction, yet exploring this capability in artificial soft swimmers remains challenging due to the high-dimensional control complexity and the computational cost of resolving hydrodynamic details. Traditional approaches often rely on morphology-dependent heuristics and simplified fluid models, which constrain exploration and preclude advanced strategies like vortex exploitation. To address this, we propose an automated framework that combines a unified, reduced-mode control space with a high-fidelity GPU-accelerated simulator. Our control space naturally captures deformation patterns for diverse morphologies, minimizing manual design, while our simulator efficiently resolves the crucial fluid-structure interactions required for learning. We evaluate our method on a wide range of morphologies, from bio-inspired to unconventional. From this general framework, high-performance swimming patterns emerge that qualitatively reproduce canonical gaits observed in nature without requiring domain-specific priors, where state-of-the-art baselines often fail, particularly on complex topologies like a torus. Our work lays a foundation for future opportunities in automated co-design of soft robots in complex hydrodynamic environments. The code is available at https://github.com/changyu-hu/FreeFlow.