Orleanist Restoration in 1871?

In 1871 the Orleanists held a majority in the National Assembly, was it possible for the French Third Republic to have become a Constitutional Monarchy? I understand that Henry the Fifth refused the throne for reasons of his own, but could Prince Philippe, Comte de Paris, have taken the throne?
 
My understanding is that there was a monarchist majority in the National Assembly, as opposed to a pure Orleanist one, and the Legitimists and Orleanists were only able to unite because the Comte de Chamborde had no children.
 
My understanding is that there was a monarchist majority in the National Assembly, as opposed to a pure Orleanist one, and the Legitimists and Orleanists were only able to unite because the Comte de Chamborde had no children.

The Orleanists were in the majority. The Legitimists were the largest minority. There was an agreement to get the Comte de Chombard, but he refused for personal reasons. If the Comte de Chombard had died by say, 1873, Philippe could've taken the throne easily.
 
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