The unprecedented hydraulic visibility of rivers surfaces deformation with SWOT satellite offers tremendous information for improving hydrological-hydraulic (H&H) models and discharge estimations for rivers worldwide. However, estimating the uncertain or unknown parameters of hydraulic models, such as inflow discharges, bathymetry, and friction parameters, poses a high-dimensional inverse problem, which is ill-posed if based solely on altimetry observations. To address this, we couple the hydraulic model with a semi-distributed hydrological model, to constrain the ill-posed inverse problem with sufficiently accurate initial estimates of inflows at the network upstreams. A robust variational data assimilation (VDA) of water surface elevation (WSE) data into a 1D Saint-Venant river network model, enables the inference of inflow hydrographs, effective bathymetry, and spatially distributed friction at network scale. The method is demonstrated on the large, complex, and poorly gauged Maroni basin in French Guiana. The pre-processing chain enables (i) building an effective hydraulic model geometry from drifting ICESat-2 WSE altimetry and Sentinel-1 width; (ii) filtering noisy SWOT Level 2 WSE data before assimilation. A systematic improvement is achieved in fitting the assimilated WSE (85% cost improvement), and in validating discharge at 5 gauges within the network. For assimilation of SWOT data alone, 70% of data-model fit is in [−0.25 ; 0.25m] and the discharge NRMSE ranges between 0.05 and 0.18 (18% to 71% improvement from prior). The high density of SWOT WSE enables the inferrence of detailed spatial variability in channel bottom elevation and friction, and inflows timeseries. The approach is transferable to other rivers networks worldwide.