A series of swift Prussian and German victories in eastern France, culminating in the Siege of Metz and the Battle of Sedan, saw the army of the Second Empire decisively defeated (Napoleon III had been captured at Sedan on 2 September). A Government of National Defence declared the Third Republic in Paris on 4 September and continued the war and for another five months, the German forces fought and defeated new French armies in northern France. Following the Siege of Paris, the capital fell on 28 January 1871 and then a revolutionary uprising called the Paris Commune seized power in the capital and held it for two months, until it was bloodily suppressed by the regular French army at the end of May 1871.

Answer this question, if possible (if impossible, reply "unanswerable"): Which army definitively defeated Napolean III?
the army of the Second Empire