The high technological and economic importance of Critical Raw Materials (CRMs) combined with geopolitical issues has led to increasing attention for CRMs used in renewable energy. It is within this framework that the French Secretary of State for Ecology, Ms. Brune Poirson, launched, on February 22, 2019, the work to develop a programming plan for low-carbon transition mineral resources. Indeed, to build the energy infrastructure essential to achieving its greenhouse gas emission reduction targets, France will need to mobilize more mineral resources, some of which may be critical. This observation is now widely shared, as evidenced by the work of the International Group of Experts on Resources, the World Bank, the European Commission. The alternative would be to reduce the dependence on CRMs, through recycling or the discovery of other technologies that do not rely on CRMs. In this paper, we investigate how the timing of the energy transition is affected by CRMs when a very costly backstop also exists. The size of the stock of CRMs may speed-up or slow down the energy transition, namely in terms of the date at which fossil resources are abandoned. In addition, most likely the results critically depend on whether recycling may effectively be used to release the stress imposed by CRMs on the energy transition.