To transition towards a carbon neutral future, we are required to look for new sources of renewable energy. The potential of the sea for capturing renewable energy is immense, but it requires us to move towards deeper waters. Therefore, there is an increased demand for research into floating renewable energy capturing devices which are accompanied by their own unique challenges. One driver in further increasing the feasibility of floating energy capturing devices is an increase of fidelity and efficiency in modeling of Fluid-Structure Interaction (FSI) problems involving free surface flows and floating bodies. One of the main issues in computational FSI for floating renewables is the need to deal with complex structural geometries. This is especially relevant in the design optimization phase, where an optimal structural solution must be defined for site-specific conditions in a limited time. Unfitted Finite Element (FE) methods are convenient for these situations, avoiding the need of ad-hoc mesh generation. The challenge here is how to deal with an unfitted structure that interacts with free surface flows. In this talk we will present a single-phase FE approach for free surface flows, where only the wave-structure interaction is accounted for, in combination with an unfitted floating structure with arbitrary geometry. In this work we propose a monolithic method with block preconditioning, ensuring robustness and efficiency of the solution. We will demonstrate the capabilities of the proposed framework with a series of tests for wave-structure interaction problems, assessing accuracy and conservation properties.