Enhancing Fossil Fuel Energy Carbon Technology Act of 2019 or the EFFECT Act of 2019 This bill directs the Department of Energy (DOE) to replace its existing fossil energy research and development technology programs with new programs. Under the new programs, DOE must research and develop fossil fuel technology for carbon capture, utilization, storage, or removal. DOE must establish a coal and natural gas technology program to ensure the continued use of domestic coal and natural gas resources through the development of technologies. The technologies must significantly improve the efficiency, effectiveness, costs, and environmental performance of coal and natural gas use. In addition, DOE must establish a research, development, and demonstration carbon storage program and a large-scale carbon sequestration demonstration program. DOE may establish an integrated storage program. DOE must also establish a carbon utilization program to identify and assess novel uses for carbon, carbon capture technologies for industrial systems, and alternative uses for coal. Finally, DOE must establish a program to develop technologies and strategies for removing carbon dioxide from the atmosphere on a large scale. The program must include air capture technology prizes provided under a competition as well as grants for centers that test direct air capture and storage technologies.