To make this more plausible then perhaps Napoleon II survives his tuberculosis after a miracle recovery. His grandfather taking pity on him allows him to serve in the Austrian Army. This gives Napoleon II experience and allows him to form connections in the Austrian army. His name if Bonaparte also allows him to have some prestige. Napoleon II was described by his contemporaries as very intelligent and charming (unlike Nappy III who people perceived as a clumsy fool). Napoleon then rises up the ranks and he’s shown himself to be a proven battle commander.I’m pretty sure that all the European Powers would applaud Louis Napoleon’s attempt to conquer Italy and turn back the clock to his uncle’s golden age
1830’s:
France is in a full Civil War because let’s say Charles X refuses to give up power and flees to the countryside to rally support against the revolutionaries in Paris. Some support Louis-Philippe as the next King of France. Let’s say instead of the 1840’s a crop failiure occurs ten years early in Central Europe which causes revolutionary movement to break out across Prussia and Austria. Maybe the Italians and Hungarians both revolt since Europe is in flames and the Austrian Government is in chaos.
Napoleon II has a contingent of army officers loyal to him and he goes to Italy where he presents himself to the Italian Nationalists. He never abdicated as King of Rome: the title Napoleon I crowned him with as an infant. He then re-assumes his title and conquered the other Italian states through his military genius. He then meets with the Pope. One of the popular and more Conservative Italian unification ideas was a confederacy led by the pope as its nominal head. Napoleon II would agree to this and would then his invite his Murat cousin to become King of Naples. The Pope would then crown Napoleon II as King of Rome and then acknowledge him as French Emperor.
Perhaps as a butterfly of this Germany unified around the Frankfurt convention or something similar. Perhaps Napoleon freaks out by this powerful enemy at his doorstep. Maybe he makes a deal with the Austrians and Bavarians. Perhaps he later crushes them with the Bavarian and Saxon army defecting to Napoleon which plows him victory. Napoleon then marches on Berlin and restores the Confederation of the Rhine. Prussia would be stripped of land while his allies would be strengthened.