Sector-level Phillips curves are estimated in French data. There is considerable heterogeneity across sectors, with vastly different estimates of the backward looking component of inflation and the duration of nominal rigidities. A multi-sector model of inflation dynamics is calibrated on the basis of these sectoral estimates. Aggregate inflation, simulated on the basis of heterogeneous sectors, displays comparable dynamics to actual data. A comparison is drawn between the policy trade-offs implied by a Phillips curve based on macroeconomic estimates vs. one based on a model with heterogeneous sectors. The difference is sizeable.