Fair Maps Act of 2019 This bill prohibits a state from establishing a congressional districting plan that unduly favors or disfavors a political party. Any eligible voter from the state may sue to invalidate such a districting plan. The bill also establishes certain required and permissible criteria for states to consider when establishing or altering congressional district boundaries, as well as criteria that states are prohibited from considering when devising districting plans. Furthermore, a state that has an approved remedial districting plan may not be redistricted again until after the next apportionment of Representatives unless a court requires the state to conduct such subsequent redistricting to comply with the U.S. Constitution, the Voting Rights Act of 1965, the state's constitution, or the terms or conditions of this bill.