We describe a simple spatial model of urban growth for systems of cities at the macroscopic scale, which combines direct interaction between cities and an indirect effect of physical network flows as population growth drivers. The model is parametrized on population data for the French system of cities between 1831 and 1999, which strong non-stationarity in correlation patterns suggest to apply the model on local time windows. The corresponding calibration of the model using genetic algorithms provide the evolution of interaction processes and network effects in time. Furthermore, the fit improvement when adding network module appears effective when controlling for additional parameters, what confirms the ability of the model to unveil network effects in the system of cities.