This paper deals with the scattering of a plane wave from a two-dimensional random thin film. For a Gaussian random disorder, a first order solution is derived explicitly by a probabilistic method. It is then found that ripples appear in angular distributions of the incoherent scattering. Furthermore, the incoherent scattering is enhanced in the directions of backscattering and specular reflection. Physical processes that yield such an enhanced scattering are discussed. Numerical examples of the coherent and incoherent scattering are illustrated in figures.