In this article we are interested in the regularity properties of the probability measure induced by the solution process of the Lévy noise or a fractional Brownian motion driven Navier Stokes Equation on the two dimensional torus $\mathbb{T}$. We mainly investigate under which conditions on the characteristic measure of the Lévy process or the Hurst parameter of the fractal Brownian motion the law of the projection of $u(t)$ onto any finite dimensional $F\subset L^2(\mathbb{T})$ is absolutely continuous with respect to the Lebesgue measure on $F$.