Does Charles III survive?
If he does, then obviously he is the heir to Parma. The Two Sicilies may still be conquered in the War of Polish Succession (assuming no butterflies) or another similar war, and the powers won't allow Spain to have a foothold in Italy, so Charles will become King of Naples and Sicily as OTL, with his Italian domains passing to his children. A PoD in 1716 allows Luis I and Fernando VI to have surviving sons, so the Spanish throne may not go to Charles at all. If it does, Spanish Italy will go to Charles' younger son(s), while if Charles never becomes King of Spain, his line just becomes an Italian cadet branch like the OTL Two Sicilies and Parma branches.
If Carlos dies young, then there is more pressure on his elder brothers to produce issue, and if they fail then Spain maybe falls into another War of Succession. With regard to Parma, the heir is either Mary of Modena (widow of James II of England, etc.) or Rinaldo d'Este, Duke of Modena. Both are descended from Ranuccio I of Parma via his two daughters, who both married the same guy. The exact line of succession depends on the exact application of semi-Salic law, but I would assume that Parma would pass to Mary's son in the same way as it worked with Charles III IOTL. BTW the new rightful successor to the Medici' as Grand Duke of Tuscany would, I think, be a member of the Orsini family, descended from a daughter of Cosimo I. This one death will therefore change the outcome of the War of the Polish Succession tremendously, and I can't really get my head around the ramifications.
OK. Cosimo III tried to leave Tuscany to the Duke of Modena, but never to the Duke of Parma, who had a better claim. Thus, he would be liable ITTL to favour Rinaldo d'Este over the much more minor Duke of Guastalla. Let's take it as read that the course of the War of Polish Succession goes generally as it did in our history, just to save our own sanity. However, instead of Carlos leading a Spanish Army from Parma to conquer Naples and Sicily, Parma instead belongs to Giacopo Stuarto, so Spain has to launch a sea-borne invasion. Additionally, there is no hope amongst the inhabitants of Naples that they will be independent of Spain under a younger brother, so Spain might come out of the war without complete control of the Neapolitan mainland.
Either Fernando VI has kids, or the throne of Spain is in crisis. This is likely to be extremely complex, due to various renunciations and the Pragmatic Sanction.
Would Britain allow James Stuart to receive Parma? I mean, wouldn't they put diplomatical pressure in order to it never to happen?
Or alternatively they demand he renounce all claim to England in exchange.
Britain didn't have much influence in the Med at this point. As far as I know they weren't a signatory of any of the various treaties over Tuscany or the Italian settlement that came from the Polish succession war. So chances are the British would bitch and make threats but really Duke James of Parma would work out quite well for them. That would make the Stuarts foreign, Italian monarchs. Basically the worst possible thing in the eyes of the British public.
OK. Cosimo III tried to leave Tuscany to the Duke of Modena, but never to the Duke of Parma, who had a better claim. Thus, he would be liable ITTL to favour Rinaldo d'Este over the much more minor Duke of Guastalla. Let's take it as read that the course of the War of Polish Succession goes generally as it did in our history, just to save our own sanity. However, instead of Carlos leading a Spanish Army from Parma to conquer Naples and Sicily, Parma instead belongs to Giacopo Stuarto, so Spain has to launch a sea-borne invasion. Additionally, there is no hope amongst the inhabitants of Naples that they will be independent of Spain under a younger brother, so Spain might come out of the war without complete control of the Neapolitan mainland.
In the Treaty of Vienna:
1) Stanislaw Leszczynski is deposed as king of Poland. He is given a replacement which will then go to France upon his death. This may as well be Lorraine.
2) Francois Etienne of Lorraine needs compensation. With Naples still being contested, it is decided that he will become King of Naples, especially since his lands will go to the Habsburgs anyway when he marries Maria Theresa. Austria therefore is denied territorial expansion in Italy. Spain gets Sicily.
3) Francesco III of Modena, whose father Rinaldo had been persuaded by his nephew, the Duke of Parma, to side against Austria, is rewarded by being recognised as heir of Tuscany pursuant to the negotiations carried out by the late Cosimo III.
If the descendants of Rinaldo or Mary of Modena die out, they are each others' heirs. This would produce a genuine counterweight to Piedmont-Sardinia in central Italy.
Either Fernando VI has kids, or the throne of Spain is in crisis. This is likely to be extremely complex, due to various renunciations and the Pragmatic Sanction.
As for the Spanish Succession issue. It is probable that Felipe V would remarry (as someone mentioned already) but it would certainly be to someone less strident, crafty and ambitious that Elizabeth Farnese (because who had more of those characteristics than her?)
Actually the house of Lorraine (the Vaudemont branch of the house of Ardennes-Metz/Chatenois) had a claim of the kingdom of Naples, which (the claim) they inherited from the house of Valois-Anjou.(...)
In the Treaty of Vienna:
(...)
2) Francois Etienne of Lorraine needs compensation. With Naples still being contested, it is decided that he will become King of Naples, especially since his lands will go to the Habsburgs anyway when he marries Maria Theresa. Austria therefore is denied territorial expansion in Italy. Spain gets Sicily.
(...)