I was re-reading through Pál Engel’s paper "The Age of the Angevines, 1301-1382" (Chapter 5 [pg. 34-53] of Peter F. Sugar's, Péter Hanák's, and Tibor Frank's [editors] A History of Hungary) and I got an idea for a PoD:
In 1343 King Robert of Naples and of Anjou of the House of Angevine, great-great-uncle to King Louis I the Great of Hungary of the House of Angevine, died. At the time, Louis' younger brother Andrew was the Duke of Calabria, the husband of Joan I of Naples, grand-daughter by his first son to King Robert. This made Andrew the natural heir to Robert. However, Queen Mother Elisabeth of Poland of Hungary, the mother of both Andrew and Louis, was just as power-thirsty as her first son and so wished to see Hungary and Naples united under one king, Louis I. Upon Robert's death she embarked with the blessing of Buda's court to Italy, where she invested five tons of gold florins and more of silver in an attempt to purchase the Neaopolitan throne for Louis. She did, in fact, manage to win the favor of the pope, Naple's overlord, but it was too late. Her second son Andrew ascended to the throne (he was quickly murdered, however, leading to two Hungarian campaigns to conquer the region in revenge, both of which failed as no southern Italian wished to see a king not bearing the Neapolitan crown on the throne).
Here is the PoD, Robert remains on the death bead for some time longer drawing out the whole process; this gives Elisabeth the necessary time to purchase the crown for her elder son. Upon Richard's death, Louis comes across the Adriatic and is crowned the legitamate King of Naples.
Having a firm grip over Naples, Louis then proceeds to use the resources he spends in his two Neapolitan campaigns in OTL plus added resources from Italy to campaign against his southern neighbours in Račka (Bosnia), Serbia, Bulgaria, and Cumania (Walachia and Moldavia). While in OTL these campaigns were unseccessful, the added resources and focus would likely make the campaigns much more successful, effectively extending Hungary deep into the southern Balkans as far as the Byzantines.
This strengthens Hungary, affirming its place. It also strengthens the Angevine line, allowing Hungary to continue its Golden Age past where in OTL the Angevine line died out and unattentive Jagellion rulership, distracted from a slowly weakening Hungary sapped of strength after the fall of its Byzantine ally, allowed Hungary to fall to pieces and be overrun by the Ottomans and Austrians. However, a strengthened Hungary would also naturally run into conflict with its long-time Byzantine ally. The Byzantine fall would thus be quickened, as a Byzantium engaged in conflict with both Hungary and the Ottomans could not last long.
Additionally, the Ottomans being forced from easy conquest of the weak Christian kingdoms as they pursied in OTL by Hungary having conquered them would turn the Ottomans away from Europe. This would turn them even more towards Africa and towards conflict with Persia. This conflict with Persia would likely trickle down to India and East Asia in some way, though I don't know quite how. Additionally, without domination of most of the Balkans, the Ottomans would lose nearly all of their Janissary forces that proved so precious in OTL, weakening them militarily.
As for Western Europe, the strengthening of Hungary would mean that the Queen Mother Elisabeth of Bosnia would have been able to prevent the marriage of her daughter Mary to Sigismund, who was destested by both, in favor of a marriage with a member of either the related Bosnian royal family or the Croatian noble family, the Frangipanis who were close friends with Elisabeth as well as part of the larger Gorjanskih clan which were the major allies of the Bosnian royal family to which Elisabeth belonged or, just as likely or perhaps more likely, carrying out of her reign indepedently. In the former case a Hungarian heir would have been produced and in the later case Tvrtko, Ban (a Hungarian noble title) of Bosnia and King of the Serbs would have succeeded to the Hungarian throne. In any case this would have fit in to Hungary's growing dominance of the Balkans, while more importantly to the west would have turned Sigismund's attention towards Germany.
Deprived of power in Hungary, he most likely would have embarked on a series of the sort of sinister political moves for which he is remembered as he reached for power in Germany. On the other hand, without the accumen and power gained while king of Hungary he may not have been in the necessary position to secure the Holy Roman Emperorship upon the death of King Rupert. How either of these scenarios would have fanned out I am not sure, but I am sure it would have been significant.