Foreign Agents Registration Modernization Act of 2019 or the FARM Act of 2019 This bill imposes additional requirements related to the public database of registrations that are filed, as required by the Foreign Agents Registration Act (FARA), by agents that engage in certain political activities for foreign principals. Specifically, the Department of Justice shall establish the National Foreign Agents Database, which shall be a publicly searchable, sortable, and machine-processable database of the information contained in such registrations. Current law requires a database of registrations to have search and sort functions only to the extent technically practicable. FARA-required registrations shall be filed in an electronic, structured data format. Electronically filed registrations shall be immediately available to the public over the internet.