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 recycling the revenue through lump-sum transfers. However, it would still generate large horizontal distributive effects. The determinants of the tax incidence are characterized precisely, and alternative targeted transfers are simulated on this basis. The paper argues that when households differ on multiple dimensions, fuel poverty can be used to identify the most vulnerable with respect to energy consumption. If public acceptance of energy taxes depends on Rawlsian considerations, it can substitute for the common focus on low-income households and be used as a better barometer of a policy's acceptability.