A.) Austria defeats Nap. III in northern Italy, after France allies with Savoy. Napoleon III's forces are decisively crushed, and the French Emperor nearly captured. in the peace treaty, France is forced to acknowledge Austrian supremecy in all matters concerning Italy, and to stay out of "The Boot." Savoy is slapped down hard - Lombardy is to be returned, and the Kingdom of Sicily is guaranteed (or restored, I forget if it had been absorbed prior to the Savoyard land grab against Austria). Likeswise, big reparations to Austria and a pledge to recognize the Austrian border. Tuscany and Modena are recognized as well.
B.) Austrian victory in the war against Prussia. Silesia regained, other concessions to her allies, the Rhineland is taken away from Prussia, with the matter to be decided by the constituent states of the German Confederation. Later on, it is awarded by them to Austria. Savoy is beaten like the proverbial red headed step child after they try to avenge their earlier defeat: Piedmont is given to one of the disposessed Italian noble families, even heavier indemnities and reparations fall on Savoy, and the Royal Family flee into exile while a republic is proclaimed. Austrian troops help to maintain order (w/explicit Austrian consent, French troops join in the endeavor and FJ allows Nap.III to expand the border into Savoy a little bit).
C.) Austria gains control of Bosnia under the same conditions as OTL. They come to an agreement concerning the Balkans in that Russia concedes Serbia and Montenegro as an Austrian sphere of interest, while Greece and Bulgaria are in the Russian zone. Handwavium, Pan Slavism never really takes off.
D.) France needs a military adventure (and easy victory) to placate or distract the masses from troubles at home, and so goes ahead with his Mexican adventure. Maximillian Habsburg reigns as Emperor.