In recent years, research in climate science has increasingly emphasized the need to reduce fossil fuel supply in order to avoid an overshoot of the global carbon budget and to meet the Paris Agreement target to keep global warming ‘well below 2°C’. This article aims to outline a balanced appreciation of the particular responsibility held by transnational oil and gas companies in the global challenge to organize an equitably managed decline in fossil fuel extraction. It does so by focusing on a case study. The latter consists of the stylized reconstruction of the internal social dynamics that shape the power structure of the French firm Total and of questioning its ability to make investment decisions aligned with the imperative to preserve the stability of the climate system, as its public position makes clear. The persistence of short-termed compensation schemes in the higher corporate hierarchy impedes the elaboration and implementation of deep decarbonization strategies at the firm level. These would imply a significant upscaling of investments in renewable energy and/or carbon-capture storage technologies, in order to avoid the foreseeable destruction of corporate jobs linked to oil and gas extraction in an increasingly carbon-constrained world.