Translation of "Highness" in French

Has her Highness slept well?

Sa Majesté a-t-elle bien dormie ?

And all you need to do, Your Royal Highness,

Tout ce que vous devez faire, Madame,

I had to cool my heels for an hour in front of the door, waiting for his highness to leave the bathroom.

J'ai dû poireauter une heure à la porte avant que monsieur ne daigne sortir de la salle de bain.

Kate Middleton is now Her Royal Highness Princess William Arthur Philip Louis, Duchess of Cambridge, Countess of Strathearn, Baroness Carrickfergus, Master of Arts.

Kate Middleton est désormais Son Altesse Royale la princesse William Arthur Philip Louis, duchesse de Cambridge, comtesse de Strathearn, baronne de Carrickfergus, maître ès arts.