This paper studies the distributional effects of France's recently introduced carbon tax. Using a microsimulation model built on a representative sample of the French population from 2012, it simulates the taxes levied on each household's consumption of energy for housing and transport. Without revenue recycling, the carbon tax is regressive and increases fuel poverty. From a policy perspective, this finding indicates that the question of fuel poverty cannot be ignored in the quest for a fair ecological transition. It proposes that some of the revenues from the carbon tax should be redistributed to households. Different designs of cash transfer to support households are then compared. The results show that the inequities of the carbon tax could be offset at reasonable cost relative to total carbon tax revenues. However, adjusting the design of cash transfers to criteria other than income level does not diminish the cost of compensating households. The benefits of finely adjusting cash transfers may therefore be somewhat limited. Most notably, the results show that targeting revenue recycling at low-income households would help to reduce fuel poverty substantially. This study therefore indicates that carbon taxation actually provides an opportunity to finance ambitious policies to fight fuel poverty.