Graphene Josephson Junctions (GJJ) in the regime of ballistic transport where current is carried by discrete energy states of Andreev-reflected coherent electron-hole pairs have been recently demonstrated in graphene heterostructures. Due to the non-linear current-phase relation, GJJ can be used as a sensitive probe of underlying microscopic noise sources. Here, we find an analytic expression for the supercurrent-phase relation in the finite low doping regime, and we sketch how a GJJ quantum circuit can play the role of noise quantum sensor.