The Council of Europe has adopted the Framework Convention on Artificial Intelligence – the first of its kind. Notably, the Framework Convention includes provisions specifically tailored to enable the EU’s participation. At the same time, the EU has developed its own framework around AI. I argue that the EU should adopt the Framework Convention, making an essential first step toward integrating the protection of fundamental rights of the EU Charter. Ultimately, this should create a common constitutional language and bridge the EU and the Council of Europe to strengthen fundamental rights in Europe.