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This paper studies how firms adjust input sourcing in response to climate policy. Using the EU Emissions Trading System (ETS) as a natural experiment and French product-level import and production data, we show that firms increasingly shifted imports of ETS-regulated inputs to non-EU countries over the 2010s as the policy became more stringent, indicating carbon leakage. This leakage is economically significant: the share of ETS-regulated products sourced from outside the EU rose by 4.3 percentage points after the ETS was implemented. Motivated by these empirical findings, we estimate a heterogeneous firm model using pre-ETS data. Simulating the model under a €100 carbon tax reproduces observed leakage, raises domestic prices and modestly reduces French emissions. Adding a carbon tariff similar to the EU’s Carbon Border Adjustment Mechanism (CBAM) reverses the leakage but further increases prices. The combined ETS+CBAM regime is seven times more effective than the ETS alone in reducing emissions.