In France, "un fonctionnaire" is "un agent de l'Etat" (state agent), employed by the central State or local State representatives. The army, the police, hospitals, schools, city halls, courts... all employ "fonctionnaires".
In a previous question in this same lesson, the given preferred translation for 'finalement' was 'at last'. Now, here, it gets marked wrong! I will report it and see what they say.