"Old Frederick" is Frederick the Great ("Alte Fritz"), and together with the colours taken at Jena and Auerstadt, Napoleon brought Frederick's sword to France. The line about "children" is metaphorical, and I would guess that it refers either to the conquered people of Prussia itself (now under Enlightened protection,you see) or to The Confederation of the Rhine, Napoleon's bringing numerous minor Germanic princedoms and little kingdoms into one state. Pretty much the same thing, though not all the population would have thanked Napoleon and "The Goddess of Freedom".

Those who were "eager to slay" Napoleon included not just the crowned heads of Europe but the oligarchy of the British State; hence the reference to "their gold through all Europe", and indeed their joining with the Mamluks, though this would be a conflation of the Battle of the Pyramids with the Battle of Alexandria, and presumably the [naval] Battle of the Nile. Since throughout the various Coalitions - against Revolutionary France and then the Napoleonic Empire and then Napoleon personally - Britain provided financial contributions to the Continental Powers for these to keep soldiers in the field, it could be argued that the exploited "lower orders" of Britain and of India, together with the slaves of the West Indies, provided the money to put the "lower orders" and serfs of Europe to war against the French Army and State, so that the citoyens of France could be returned to the condition they had endured before the Revolution. The song's reference to the Goddess of Freedom is pointed.

Perhaps the "Empress" might have sought Boney in South America, at least in spirit.