Survival of Simon de Montfort

What if during the siege of Toulouse Simon de Montfort doesn't die, and the mangonel misfires and breaks down instead. Will Simon be able to settle the Toulouse question permanently? Thus averting Louis VIII's death from dysentery after assaulting Toulouse again.

Another thing that comes to mind is the Reign of Simon de Montfort. How would an ultra orthodox Catholic rule Toulouse?
 
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