On the 9th of August 1832 a retired army captain, Franz Reindl, furious at having been refused a sum of money he had requested, made an attempt on... edit: Archduke Ferdinand, heir to the throne of the Austrian Empire and at least partially mentally disabled.
Iotl Ferdinand survived with a negligible wound, but what if he had died? In these circumstances would Franz Karl accept the throne? Probably yes as there aren't many alternative around.
What was his character like? I couldn't find much, given his irrilevance post-abdication...
He probably wasn't too bright, but probably capable enough to avoid a regency council?
Avoiding 13 years of ineffectual regency government seems a good thing for Austria and maybe tgings can still be patched up in Lombardy-Venetia and Hungary, possibly even avoiding the worst of 1848, but Franz Karl hardly seems an inspired reformer and certainly there would be no support for things like a comprehensive land reform in Hungary. Even the creation of an Habsburg Zollverein analogue including the southern German states as well as the Italian Duchies seems far fetched at this stage, but it would be very important to create the economic basis of a long lasting Mittleuropa.
An useful secondary POD would be an early death of Sophie (in childbirth?), so that her extremely rigid outlook on life doesn't influence Franz Josef too much. On the other side eliminatingbhwr wouod likely weaken Franz Karl faculties even more...
Edit: it is likely that Sophie would become the de facto ruler of the Empire if Franz Karl is Emperor, would this be a disaster or could her reactionarism be somewhat tempered into a less miopic form of conservatism?