As we all know Franz II (Ferdinand) decided to federate the Monarchy came only to the throne if s Maximilian and Empress Charlotte had no offspring.
Franz Josef would have married soon (probably Helene of Bavaria) - there might have been a Crown Prince - and its unlike that this one would have been as liberal as Franz II - OK Franz was not liberal, but he had a good grasp of things that were necessary - a streak the HAbsburgs are not famous of.
So I bet at the first opportunity the Hungarians would have revolted again.
I also believe that Franz Josef would NEVER have given up Lombardo Venetia without war - And we know Max did exactly that - He arranged a marriage between his younger brother Victor and Marie Chlotilde of Savoy. Not the happiest marriage, but creating Lombardo Venetia as Kingdom for them forged anto this day lasting Alliance between the House of Savoy (Now kings of Italy) and HAbsburg.
Imagine if Savoy was allied with France and or Prussia.
I am wondering if Franz Josef would have been as decisive and helped Russia win the Crimean war? It was a proud day for the Austrian army when they drove the attacking French and British troops into the sea at Sevastopol.
Indecisive as Franz Josef prooved to be he might have sat out the war making enemies with Russia and the Anglo-French alliance...