The short answer
There is no contemporary evidence that Marie Antoinette ever said this. The anecdote appears in Jean-Jacques Rousseau's Confessions, written around 1765 and describing an unnamed great princess. Marie Antoinette was a child living in Austria at the time and did not become queen of France until 1774. The chronology alone makes her an unlikely source.
How a stock anecdote found a target
The story was already a floating literary device — a shorthand for aristocratic ignorance, told about various unnamed noblewomen before it was ever told about her. What changed was the politics. During the Revolution, a foreign-born and deeply unpopular queen made a perfect vessel for an anecdote that captured what people already believed. The quote did not create the hatred; it gave the hatred a sentence.
Why this case matters more than the others
Most misattributions are harmless drift. This one is a reminder that quotations are also weapons. Attaching words to a person can make an abstract resentment feel personal and proven, and once attached the words are almost impossible to remove — the correction never travels as far as the accusation. Two and a half centuries later, the line is still the first thing most people know about her.
The lesson for readers of quotes
Ask who benefits from an attribution. A quote that conveniently confirms what an audience already wants to believe about someone deserves more scrutiny than one that surprises them, not less. This is as true of a screenshot circulating today as it was of a pamphlet in 1789.
What this means for your English
The phrase now functions as an English idiom meaning a callous, out-of-touch response to hardship. You can use it that way freely — “that's a bit let-them-eat-cake” — as long as you know it is an idiom rather than a historical record. Knowing the difference between what a phrase means and where it came from is a genuinely advanced level of the language.