This paper proposes a micro-simulation assessment of the distributional impacts of the French carbon tax. It shows that the policy is regressive, but could be made progressive by redistributing the revenue through flat-recycling. However, it would still generate large horizontal distributive effects and harm a significant share of low-income households. The determinants of the tax incidence are characterized precisely, and alternative targeted transfers are simulated on this basis. The paper shows that given the importance of unobserved heterogeneity in the determinants of energy consumption, horizontal distributive effects are much more difficult to tackle than vertical ones.