Fight for a Modern Minimum Wage Act This bill raises the minimum wage and provides for a regional minimum wage. Employees who are paid the minimum wage shall be paid at a rate of (1) $8.50 an hour beginning on January 1, 2020; and (2) five years after such date and quinquennially thereafter, the amount determined as the minimum wage rate under a formula prescribed by this bill. The bill provides for a regional minimum wage rate for a state or locality set by the Department of Labor if (1) such state or locality opts for such rate and notifies Labor, and (2) such rate is not less than the minimum wage rate that is in effect on January 1, 2020.