No, Antoine would be French.
Her mother was Maria Theresa and she and all her sisters had the first name Maria. Her name was Maria Antonia. Marie Antoinette was what her name was changed to when she married the dauphin of France, because Marie Antoinette is the French version of Maria Antonia. As a child, she went by Antonia (because she and all her sisters had the same first name), so as a French name, Antoine would be the equivalent of Antonia. That's most likely where is came from.
Nathalie Antonia's birth name is Nathalie Antonia.
Antonia Franceschi's birth name is Antonia Franceschi.
Antonia Novello's birth name is Antonia Coello.
Antonia Rey's birth name is Antonia Francesch.
Antonia Brico's birth name is Antonia Louisa Brico.
Antonia Dauphin's birth name is Antonia Beresford Dauphin.
Antonia Dorian's birth name is Aphrodite Antonia Dorian.
Antonia Prebble's birth name is Antonia Mary Prebble.
Antonia Jones's birth name is Antonia Maria Benyovszky.
Antonia Fraser's birth name is Antonia Margaret Caroline Pakenham.
Antonia di Carlo's birth name is Antonia Catriona McIvor.