The quality of the water from a riverbank well field is the result of the mixing ratios between the surface water and the local and regional groundwater. The mixing ratio is controlled by the complex processes involved in the surface water–groundwater interactions. In addition, the drawdown of the groundwater level greatly determines the water head differences between the river water and groundwater, as well as the field flowpath inside the alluvial plain, which subsequently impacts the water origin in the well. In common view, groundwater flows from both sides of the valley towards the river, and the groundwater divide is located at the middle of the river. Here, we studied the standard case of a river connected with an alluvial aquifer exploited by a linear pumping field on one riverbank, and we proposed to determine the physical parameters controlling the occurrence of groundwater flow below the river from one bank to the other (cross-riverbank flow). For this purpose, a 2D saturated–unsaturated flow numerical model is used to analyze the groundwater flowpath below a streambed. The alternative scenarios of surface water–groundwater interactions considered here are based on variable regional gradient conditions, pumping conditions, streambed clogging and the aquifer thickness to the river width ratio (aspect ratio). Parameters such as the aspect ratio and the properties of the clogging layer play a crucial role in the occurrence of this flow, and its magnitude increases with the aquifer thickness and the streambed clogging. We demonstrate that for an aspect ratio below 0.2, cross-riverbank flow is negligible. Conversely, when the aspect ratio exceeds 0.7, 20% of the well water comes from the other bank and can even exceed the river contribution when the aspect ratio reaches 0.95. In this situation, contaminant transfers from the opposite riverbank should not be neglected even at low clogging.