Current noise is measured with a SQUID in low impedance and transparent Nb-Al-Nb j unctions of length comparable to the phase breaking length and much longer than the thermal length. The shot noise amplitude is compared with theoretical predictions of doubled shot noise in diffusive normal/superconductor (NS) junctions due to the Andreev reflections. We discuss the heat dissipation away from the normal part through the NS interfaces. A weak applied magnetic field reduces the amplitude of the 1/f noise by a factor of two, showing that even far from equilibrium the sample is in the mesoscopic regime.