Foreign Agents Registration Modernization and Enforcement Act This bill amends the Foreign Agents Registration Act of 1938 (FARA) to provide that whenever the Department of Justice (DOJ) has reason to believe that a person or enterprise may be in possession or control of documentary material relevant to an investigation under FARA, the DOJ, before initiating a civil or criminal proceeding with respect to the production of such material, may serve a written demand upon the entity to produce the material for examination. The bill includes social media communications under information that foreign agents must file with DOJ. Under certain circumstances, social media communications are exempted from the requirement for foreign agents to include a disclosure statement in informational materials. Informational materials disseminated by a foreign agent as part of an activity that would not require registration, need not be filed. The FARA Registration Unit shall submit a semiannual report to Congress regarding the administration of FARA, including the number of investigations initiated based upon a perceived violation and the number of such investigations that were referred to DOJ for prosecution.