In my own opinon, it's pretty complicated to make a War of French Succession happen by 1774. For that, you have to kill the last Direct Bourbons, which are Louis XVI, Louis XVIII (at the time only Count of Provence) and Charles X (at the time only Count of Artois). And then comes the next issue which is the Treaty of Utrecht...
To most of Europe, Utrecht was the only way to prevent a Personnal Union between France and Spain. It thus banished the bloodline of Philip V of Spain from the throne, which would make the line of Orléans has the next one to rule France (meaning Duke Louis-Philippe, his son (OTL Philippe Egalité) or grandson (OTL Louis-Philippe I, King of the French) by our time period). The transition will thus probably go that way because Europe will want it to be so. Add to this that Philip V's heirs are Kings of Spain and that the French had a Hundread Years War because they didn't want an English King and you get the picture...
It could be possible however that Charles III of Spain could make a claim on the throne because he is the senior Bourbon. By 1774, Charles III already had two sons who could suceed him: the future Charles IV of Spain and Ferdinand I of the Two-Sicilies. He even had a third son, Gabriel. Charles III could argue he should be the King of France with his son Charles inheriting the French crown, Ferdinand the Spanish one and Gabriel that of the Two-Sicilies. But would he really go to war over the throne of France?