He would not go to Sarajevo, so he wouldn't be killed of, so WW1 won't happen for that reason. When it comes to reforming the empire, I'm not sure if he had the will or the ability to do anything more than cosmetic reforms. (Not to mention the Habsburg family saw two parliaments as two too many, no way they'd accept even more of them).
And of course the Hungarian question, to try to reform without pissing of the Hungarians is like trying to steal honey from a bee hive without getting stung.
IMHO, there is no such thing as "cosmetic reforms" in Austria-Hungary. Either you reform big-style, or you do it the Franz Josef way: diligently keeping things clean, but careful not to move the furniture.
I think it is quite well-established that for some unexplicable reason, FF saw a South-Slav 3rd party as the main project after his ascendancy to the throne.
That is a problematic project, but anything more than a cosmetic reform. In fact, it cannot happen without a complete overhaul (or cancellation) of the post-1867 dualism. As the government of Transleithania is dead-set against giving up an autonomous, but large part of its realm, this can only be achieved by a Royal Putch in Budapest.
His antagonism against the Hungarians is beyond doubt, so I think that he wouldn't be worried about "pissing them off". I suspect he might even enjoy it.
By the way, which nationality within the monarchy would feel sympathetic to the Hungarian cause? Also, he would establish universal suffrage in Hungary, so the whole power-arrangements there would shift. Social issues would suddenly be on the agenda and compete with the national cause.
In my assessment, FF would take a big risk by running wild in Budapest - but if he doesn't blunder the action itself and follows it by further reforming the monarchy into a federation of more states (3, later 4 or even more) with slightly less autonomy than Transleithania enjoyed (that means especially no own armed forces - FF didn't trust the Honved - although during the Putch he would of course play the card of being their sovereign and order them to stay put).
Interestingly, the central government was almost autocratic still in 1914; only the two halves had their own Parliaments.
With more Parliaments (Vienna, Budapest, Zagreb....Prague.....Cracow), their importance would shrink. I expect FF to delay reforms leading to opening the can of worms of a central Parliament (the one in Cisleithania was utterly disfunctional and would benefit well from getting the Czechs out, the one in Transleithania was rigged and thus mainly represented the Hungarian elites). I rather expect some sort of Imperial Council similar to the EU commission (a cabinet of appointees of the single "crowns") during his reign.
A proper "Danubian" Parliament might wait well into the mid-20th century. Perhaps Otto introduces it.
In such a shape, AH would be fit to last into the 21st century if it doesn't lose a world war in a desastrous way* and also manages to solve the Czech position within the monarchy in a matter with with a majority of the Czech can live after a few years.
*a moderate loss which results in getting rid one or several ethnic minorities (Romanians, Italians, Polish, Ukrainians) might actually strengthen the monarchy
)I also think he would have pushed for a third crown - and it would be a southern one - pring Croatia loose of Hungary and creating a "Yugoslav Habsburg Kingdom".
