Not sure how likely this is, but I'll try.
Austria wins in Italy in 1859. They restore the monarchs of central Italy as puppets of Vienna and curtail Sardinian influence in the region. France is humiliated and Austria continues its reactionary policies, while France is seen as a crusader for national unification. Whatever PoD let the Austrians do this (maybe Bach doesn't ignore military industry while he's in power) also lets them beat the Prussians (and maybe the Sardinians, who are likely itching for a third round with Austria). Prussia loses, preferably decisively, and the Austrians cement their position as hegemon of the southern German states. Germany is still formed, but without Bavaria, Wurtemburg, Baden, Saxony and maybe Silesia- basically a slightly smaller version of the North German Federation, but without the pretense of not just being a bigger Prussia.
Meanwhile butterflies cause Napoleon, Prince Imperial to die around this time. Napoleon III has no more children and dies soon after his son, his grief exacerbating his historical health issues. The emperor's death so soon after the heir's death throws the succession into chaos, which the Republicans use to stage a coup and take power, declaring the Third Republic in the late 1860s.
Without a border with Alsace-Lorraine, there's likely to be a lot less noise over irredentists in this alternate Germany. Germany and France ITTL also have a common enemy- Austria (or Austria-Hungary, they still might do this to placate the Magyars). Meanwhile the Austrians remain too focused on keeping north Italy and southern Germany as their playground to make much fuss about the Balkans. They make some gains and make sure that the states bordering them sign treaties of neutrality with Austria, but mostly they keep their focus west, preventing conflict with Russia.
Ultimately Europe erupts into a war between the liberal(ish) nationalists and the reactionary imperialists, with the sides being the Western Powers (Germany, France, Sardinia) and the Imperial Allies (Austria/Austria Hungary, Russia, whatever balkan satellites Russia has and maybe Spain if butterflies give the Carlists a victory there). Britain stays neutral, but the fighting is ferocious. By the end of the war the Allies collapse into exhausted nation-states, and Italy and Germany are fully unified. Due to spending so much blood and treasure fighting alongside France, the French claims on Alsace Lorraine are conveniently ignored when Germany makes their territorial demands at the peace. France, Germany and Italy work together to rebuild the shattered remnants of the Eastern European empires (and maybe Spain) into friendly regimes through their political and economic guidance. Everything is going well, until the great Eastern Revolution births the United Socialist Republics of the Intermarium...