Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterparts, including cascade of excitations across length scales. In two dimensions, the existence of a range of length scales (the inertial range) over which kinetic energy is transferred from small to large length scales is known as an inverse energy cascade and has been observed in several classical systems from soap films to Jupiter's atmosphere. For quantum fluids, there has been a long debate about the possibility of these inverse cascades, and while recent works suggest their existence, the microscopic mechanism is still debated and a direct experimental observation is still missing. In this work, we report a direct experimental signature of a flux of kinetic energy from small to large length scales in a quantum fluid of light and the observation of a Kolmogorov scaling law in the incompressible kinetic energy spectrum. The microscopic origin of the algebraic exponents in the energy spectrum is understood by studying the internal structure of quantized vortices within the healing length and their clustering at large length scales. Finally, we identify the statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices. These results are obtained using two counter-streaming fluids of light, which allows for a precise preparation of the initial state and the in-situ measurement of the compressible and incompressible fluid velocity. This novel platform opens exciting possibilities for the study of non-equilibrium turbulence dynamics in reduced dimensions with a controlled forcing mechanism and an homogeneous density.