We compute the correlation function of a superconducting order parameter in a continuous model of a two-dimensional Josephson-junction array in the presence of a weak Gaussian noise. When the Josephson coupling is large compared to the charging energy, the correlations in the Euclidian space decay exponentially at low temperatures regardless of the strength of the noise. We interpret such a state as a collective Cooper-pair insulator and argue that it resembles properties of disordered superconducting films.