Greigite (Fe3S4), with its ferredoxin-like 4Fe-4S redox centres, is a naturally occurring mineral capable of acting as a catalyst in the conversion of carbon dioxide (CO2) into low molecular-weight organic acids (LMWOAs), which are of paramount significance in several soil and plant processes as well as in the chemical industry. In this paper, we report the reaction between CO2 and water (H2O) to form oxalic acid (H2C2O4) on the partially oxidised greigite Fe3S4(001) surface by means of spin-polarised density functional theory calculations with on-site Coulomb corrections and long-range dispersion interactions (DFT+U-D2). We have calculated the bulk phase of Fe3S4 and the two reconstructed Tasker type 3 terminations of its (001) surface, whose properties are in good agreement with available experimental data. We have obtained the relevant phase diagram, showing that the Fe3S4(001) surface becomes 62.5% partially oxidised, by replacing S by O atoms, in the presence of water at the typical conditions of calcination [Mitchell et al. Faraday Discuss. 2021, 230, 30-51]. The adsorption and co-adsorption of the reactants on the partially oxidised Fe3S4(001) surface are exothermic processes. We have considered three mechanistic pathways to explain the formation of H2C2O4, showing that the coupling of the C-C bond and second protonation are the elementary steps with the largest energy penalty. Our calculations suggest that the partially oxidised Fe3S4(001) surface is a mineral phase that can catalyse the formation of H2C2O4 under favourable conditions, which has important implications for natural ecosystems and is a process that can be harnessed for the industrial manufacture of this organic acid.