We present a theory of thermal electronic noise in a polycrystalline metallic film the thickness a of which is comparable to the intrinsic or bulk electron mean-free path I,,. It is assumed that the film consists of grains with an average size d larger than or equal to a. Within the model including background, grain-boundary and external-surface electron scattering we have calculated the autocorrelation function and spectral density of the thermal noise as a function of the ratio l(0)/a and the value of the grain-boundary scattering parameter a depending on l(0)/d and on the grain-boundary reflection coefficient R. The results of the calculation for purely diffuse surface scattering show a substantial deviation of thermal noise characteristics from those in bulk monocrystalline materials. We have found that with the increase of the parameters l(0)/a and/or alpha the autocorrelation function becomes non-exponential and the noise spectrum deviates from the standard Lorentzian shape. The following features of the fluctuation spectrum are predicted and can be verified experimentally: (i) the redistribution of noise power over the spectrum, namely, the suppression of the low-frequency fluctuations and an increase of the magnitude of noise in the high-frequency region; and (ii) a considerable 'blue' shift of the cut-off frequency in the noise spectrum.