  We study mesoscopic fluctuations and weak localization correction to the
supercurrent in Josephson junctions with coherent diffusive electron dynamics
in the normal part. Two kinds of junctions are considered: a chaotic dot
coupled to superconductors by tunnel barriers and a diffusive junction with
transparent normal--superconducting interfaces. The amplitude of current
fluctuations and the weak localization correction to the average current are
calculated as functions of the ratio between the superconducting gap and the
electron dwell energy, temperature, and superconducting phase difference across
the junction. Technically, fluctuations on top of the spatially inhomogeneous
proximity effect in the normal region are described by the replicated version
of the \sigma-model. For the case of diffusive junctions with transparent
interfaces, the magnitude of mesoscopic fluctuations of the critical current
appears to be nearly 3 times larger than the prediction of the previous theory
which did not take the proximity effect into account.
