Fumaric acid is a promising monomer to obtain biomass-based polyesters and polyamides, and it is mainly produced by fungi of the Rhizopus genus in medium to high titters. The use of glucose, a main component of starchy and cellulosic food waste, as carbon source, together with a low-nitrogen source concentration, is a promising route to reduce process costs. In this work, the effects of nitrogen and carbonate sources on Rhizopus arrhizus NRRL 1526 morphology and fumaric acid productivity were analysed, simplifying the traditional production broth composition. Moreover, a non-structured, non-segregated kinetic model was proposed and fitted to concentration data of all relevant components obtained in batches performed in triplicate with the selected production broth at 34 °C and 200 rpm in an orbital shaker.