A poster on soc.history.what-if argued (sorry, the URL is no longer working) on the old "what if the Count of Chambord accepted the tricolor" question:
"I have always seen it as more than simple stubbornness. He was a traditionalist and had little love for the modernistic profiteers of revolution he saw in the Orleanist line. Why should he leave his tranquil exile home in Austria and become king for the probably short rest of his life, when in the grand view this only meant enabling the Orleanist heirs-of-regicides? IMO the flag issue was just the symbol, not the reason.
"Having Chambord die before 1870 and the Legitimist line extinct in 1871, thereby uniting the claims (save the Carlist ones, which no one in France took seriously) looks like a vastly better way to restore Bourbon monarchy - the offer is made to the one remaining claimant, the comte de Paris, to become the "King of the French".
"Again, IMO, a constitutional Orleanist monarchy after 1871 with tricoleur and 1831 coat of arms...would probably look a lot like the Third Republic in nearly all important regards, except perhaps for a bit (but not that much) less anti-clericalism, and might survive to the current day just like the monarchy in the Netherlands and Belgium has."