Federal Employee Paid Leave Act This bill provides paid family leave for certain federal employees in all instances covered by the Family and Medical Leave Act, which currently only guarantees unpaid leave for such instances. Specifically, the bill requires that the 12 weeks of administrative leave to which certain federal employees are entitled for family care be paid leave. This applies to all federal employees in the competitive service (all civilian positions in the executive branch, all positions in the legislative and judicial branches, and all positions in the government of the District of Columbia), congressional employees, Government Accountability Office employees, employees who are members of the National Guard or Reserves, and certain Transportation Security Administration employees. The Office of Personnel Management is authorized to increase the amount of paid parental leave available to such employees to a total of 16 administrative work weeks.