We build, calibrate and simulate a stylized energy-economy model designed to evaluate the magnitude of carbon tax that would allow the French economy to reduce by a factor of four its CO2 emissions at a forty-year horizon. We estimate the substitution possibilities between fossil energy and other factors for households and firms. We build two versions of the model, the first with exogenous technical progress, and the second with an endogenization of the direction of technical progress. We show that if the energy-saving technical progress rate remains at its recent historical value, the magnitude of the carbon tax is quite unrealistic. When the direction of technical progress responds endogenously to economic incentives, CO2 emissions can be reduced by more than that allowed by the substitution possibilities, but not by a factor of four. To achieve this, an additional instrument is needed, namely a subsidy to fossil energy-saving research. The redirection of technical progress, which is a driver of energy transition, comes at a small cost in terms of the overall growth rate of the economy.