We present an experimental study of coherent backscattering (CBS) of photon noise from multiple scattering media. We use a pseudothermal light source with a microsecond coherence time to produce a noise spectrum covering a continuous transition, from wave fluctuations to shot noise over several MHz. The angle-dependent Fano factor of backscattered light shows an enhancement due to CBS in the wave fluctuation regime. The CBS line shape and enhancement factor of the noise power is consistent with theory in the weak-scattering limit and for a large number of open reflection channels. These initial experiments on weakly scattering media demonstrate that sensitive noise measurements can be combined with the separation of path lengths present in CBS, opening up new experiments on noise transport in the localization regime.