Carbon capture and utilisation is one of the most promising techniques to minimize the impact of the increasing amount of carbon dioxide in the atmosphere. Recently, the mineral greigite was shown to be capable of catalysing CO2 conversion, leading to useful small organic molecules. Here, we have carried out a systematic study of the adsorption and selective reduction of CO2 on the Fe3S4{111} surface. We have considered both formate and hydrocarboxyl key intermediates, leading to different reaction pathways via Eley-Rideal and Langmuir-Hinshelwood mechanisms, and we have built a kinetic model considering the wide range of intermediates in the reaction network. Our results show that the mechanism to produce formic acid takes place via formate intermediate mostly on FeA sites, while methanol is formed via hydrocarboxyl intermediates on FeB sites. From the kinetic model, we have derived a reaction constant comparison and determined the limiting step rates. The overall process takes place under very mild conditions, requiring only a small energy input that might come from a chemiosmotic potential.