I think she actually DID say something like “Let them eat cake,” but it didn’t mean what people think it means.
Cheap bread was price controlled in Paris, and, if the bakers ran out, they had to sell more expensive items, like cake, at the same price as the cheap bread. Hence “Let them eat cake.”
100 years before her it was reputedly said by Marie-Thérèse, the wife of Louis XIV; and this was most likely the “great princess” that Rousseau was making reference to.
Whatever the translation of the french - nothing of the kind was reportedly said by Marie Antoinette during her lifetime - even by the French Revolution (mia culpa) which had every reason to demonize her.
The misattribution of the quote is apparently a modern invention based upon Rousseau's comment and an anachronistic understanding that the “great princess” was her, rather than Marie-Thérèse.