This paper studies the effect of transportation networks on spatial inequalities and redistribution within metropolitan areas. To do so, I build and calibrate a spatial equilibrium model of a city that features non-homotheticities and worker heterogeneity, allowing to capture rich patterns of workers sorting on commute costs and amenities. I then calibrate the model to the Paris urban area and use counterfactual simulations to study the effects of a) the Regional Express Rail and b) restricting car use in the city center. I find that on top of having a strong contribution to suburbanization and reducing welfare inequalities, the public transport network reduced income segregation in the area. Turning to the prospective effects of banning cars in the city center, the model predicts a reduction of the income disparities between Paris and its suburbs, at the cost of a substantial welfare loss.