I like the name the Bourbon Empire or Bourbon Realm. If anybody has any issue with a nation named after a dynasty, take it up with the Turks.
The Bourbon Realm would probably be divided into an Ausgleich-like arrangement, as an absolutist centralized rule of a country that large would be impossible. If we are excluding Italy, then I think we'd see the Bourbon Realm divided into France, Navarre, Castille, and Aragon. If we include Italy, then Sicily and Naples would be two additional crowns. Maybe the Spanish Netherlands are made part of France, maybe they remain Spanish.
If the Spanish Military is reorganized along French lines and integrated with that of France, that's a behemoth. Looking at Wikipedia for populations in 1700...
France - 21.5 million
Spain - 7 million
Spanish Netherlands - 3.1 million
Naples - 2.5 million
Sicily - 0.7 million
Bourbons in Europe Total - 34.8 million
I couldn't find info for Sardinia, Milan, or Parma and assume Presidi is included with Naples. If those are separate, then the number is higher.
In contrast...
Britain and Ireland - 8.7 million
Russia - 14 million
Poland - 9 million
Austria - 8.4 million
Portugal - 2.3 million
Holy Roman Empire - 15 million
Dutch Republic - 1.8 million
Prussia - 1.5 million
Denmark and Norway - 1.3 million
Swiss - 1.3 million
Sweden - 2.5 million
Ottomans - 24.8 million.
The Bourbons and Ottomans nearly equal the rest of Europe combined. Oomph.