The present work considers the dramatic changes the COVID-19 pandemic has brought to the global economy, with particular emphasis on energy. Focusing on the European Union, the article discusses the opportunities policy makers can implement to reduce the climate impacts and achieve the Paris Agreement 2050 targets. The analysis specifically looks at the fossil fuels industry and the future of the fossil sector post COVID-19 pandemic. The analysis first revises the fossil fuel sector, and then considers the need for a shift of the global climate change policy from promoting the deployment of renewable energy sources to curtailing the use of fossil fuels. This will be a change to the current global approach, from a relative passive one to a strategically dynamic and proactive one. Such a curtailment should be based on actual volumes of fossil fuels used and not on percentages. Finally, conclusions are preliminary applied to the European Union policies for net zero by 2050 based on a two-fold strategy: continuing and reinforcing the implementation of the Renewable Energy Directive to 2035, while adopting a new directive for fixed and over time increasing curtailment of fossils as of 2025 until 2050.