In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.