This paper investigates how firms adapt their sourcing of clean and dirty inputs in response to changes in climate policy. We use information from the European Union's Emissions Trading System (EU ETS) and the Carbon Border Adjustment Mechanism (CBAM) to create a new classification of clean and dirty products based on whether they are subject to a domestic or a border carbon tax. We then combine this dataset with French firms’ product-level import data over 2000–2019 and estimate that firms’ propensity to import dirty inputs from non-EU countries increased in the 2010s, reflecting carbon leakage. A heterogeneous firm model is then used to quantify the impact of changes in firms' sourcing of clean and dirty inputs given the implementation of a carbon tax and a carbon tariff. The simulated ETS carbon tax scenario is able to match leakage observed in the data and leads to a higher price level and a modest decline in emissions. The scenario that further includes the CBAM carbon tariff reverses carbon leakage at the cost of an additional rise in prices. Overall, household welfare declines because the higher costs associated with the carbon policies outweigh the benefits of reduced emissions. This result holds even when considering values of the social cost of carbon up to €1500.