I don't know how much the reign of Monsieur* would turn out and how much it would differ from that of his brother, the OTL Sun King. I'm not sure how Philippe d'Orléans would rule : his descendants were regarded as liberal but there is no telling how much Louis XIV's brother was. Plus, during the reign of his brother, he was vastly overshadowed by him (well, who wouldn't have been?) and thus we know few things about his ideas. He could be a great mecene though: he was already one as Duke of Orléans OTL.
I don't know how much Monsieur's homosexuality would play around... It would probably cause a few scandals in the European courts, but that itself wouldn't be a threat for the bloodline: Philippe d'Orléans had six children from two marriages OTL. However, it could be used as a weapon by the House of Condé: since Gaston d'Orléans has no sons, the Condé are the next-in-line for the throne after Philippe d'Orléans. And given how the Condé acted during the Fronde, Monsieur as King would have to watch out.
I'm also guessing that Philippe d'Orléans (King Philippe VII of France in this scenario) would probably marry Maria Theresa of Austria, the Infanta of Spain that was Louis XIV's wife OTL. After all, it was decided that she would marry a French prince with the Treaty of the Pyrenees. It would thus lead to an ATL Bourbon dynasty in France, and Henrietta of England and Elisabeth Charlotte of the Palatinate (the two wives of Monsieur OTL) would be available brides for other European princes.
*Monsieur was how you called the younger brother of the King of France. As a result, Philippe d'Orléans was often called this while he was young.