Floating offshore wind turbines pave the way to accessing deep-water regions with abundant wind resources. However, they face specific control challenges, such as the negative damping problem and increased model complexity. Since model-based control is becoming increasingly demanding, a model-free, data-driven approach is considered. Additionally, floating wind turbines are susceptible to rough environmental disturbances. Feedforward information, such as wave elevation measurements from wave radars, may be included in the controller to lessen the impact of disturbances. Although waves have been shown to increase rotor speed oscillations and turbine loads, wave-preview-based methods have only recently been explored. To this end, this paper first proposes a modified Data-enabled Predictive Control formulation that includes past and future information about measurable disturbances. The feasibility of this control strategy is then demonstrated for floating wind turbines through mid-fidelity simulations. The model-free, feedforward controller uses a preview of wave forces acting on the floating platform and aims for rotor speed regulation. Simulations indicate that the data-driven approach has potential for floating wind turbine control, and including wave feedforward action reduces the amplitude of rotor speed oscillations.