The King is dead. Long live... oh, he's dead too.

http://en.wikipedia.org/wiki/Louis,_Dauphin_of_France_(1729–1765)#Early_life_and_education

He was bitterly disappointed when his father would not permit him to join the 1744 campaign in the War of the Austrian Succession. When his father became deathly ill with fever at Metz, Louis disobeyed orders and went to his bedside. This rash action, which could have resulted in the deaths of both Louis and his father, resulted in a permanent change in the relations between father and son.

WI both the king and the dauphin died within a short time of each other?
 
Austria probably wins the war as France would drop out to deal with the Orleanists trying to grab power and some other folks probably trying too. Prussia gets nipped in the bud.
 
There should be a clear order of succession, I am guessing Louis d'Orléans, second cousin of Louis XV's father would be first in order. He was a prince du sang (prince of the blood) and the only viable candidate. While the Duke of Burboun, Henri Louis might have wanted to say something about it, he died in 1736 and his son was only 8 years old in 1744.

So, Louis d'Orléans inherits. There is no conflict regarding succession.
 
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