We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.