Combined sewer systems are spread across Europe, North America and beyond. However during heavy rainfall, they become saturated and discharge untreated wastewater into waterbodies through combined sewer overflows (CSOs). The relationship between rainfall and CSO discharge is complex and poorly understood because of underlying dynamics of the sewer system and a lack of high-frequency CSO measurements. We present a methodology to model CSO discharge from rainfall characteristics. It is tested on 22 CSOs outputs in the Seine River in Paris monitored over four summer seasons (June–September) from 2020 to 2023 using the data of 5 rain gauges. Beyond good predictive performance of the model, results show that (i) overflow peaks are well represented by a triangular hydrograph, (ii) a ramp function can predict peak size (total volume and maximum overflow) from rainfall characteristics and (iii) better prediction performances is achieved using multiple rain gauges instead of nearest gauge only. Further results show a map of CSOs response to the spatial distribution of rain, providing hints about functioning of the sewer system. This first end-to-end model can be readily applied to any sewer networks as it is lightweight and easy to train. It can support CSO discharge operational forecasting and the development of data-driven models by guiding their architecture design.