Global Nuclear Energy Assessment and Cooperation Act This bill establishes requirements concerning international nuclear energy cooperation and safety. Specifically, the Department of Energy (DOE) must develop and carry out a program to train foreign nuclear energy experts and standardize safety practices. DOE must also study the global status of the civilian nuclear energy industry and its supply chain. In addition, the bill prohibits any person from possessing or owning enriched uranium from Russian or China unless specifically authorized by the Nuclear Regulatory Commission (NRC). NRC may not issue a license to possess or own such fuel if DOE and the Department of State determine that the possession or ownership would pose a threat to national security. NRC must establish an International Nuclear Reactor Export and Innovation Branch within its Office of International Programs to carry out and coordinate certain nuclear reactor export and innovation activities. NRC must also identify in its annual budget justification such activities.