In many global cities the rental housing market is partially regulated. We document that the Paris housing market is dual: a flexible rent sector coexists with a large controlled rent sector. The two sectors have very different rent gradients towards the center of the agglomeration. We develop a model explicitly accounting for these features which allows to investigate general equilibrium effects of rent controls at the city level. In this framework the coexistence of a controlled and flexible rent sector increases the spatial misallocation of households. This mismatch can generally be alleviated by an improvement in urban transport infrastructures.