As far as we know, she never saying anything resembling "Qu’ils mangent de la brioche", but was despised by enough of the French public (for the high crime of being - gasp! - Austrian) that it stuck to her with relative ease.

The phrase itself - and the associated sentiment of depicting an out-of-touch aristocrat completely unconcerned with the suffering of her people - actually pre-dates Marie's tenure as La Reinne du France - going back to the 1765 publication of Jean-Jacques Rousseau's Confessions, in which he wrote in Book 6:

Enfin je me rappelai le pis-aller d’une grande princesse à qui l’on disait que les paysans n’avaient pas de pain, et qui répondit : Qu’ils mangent de la brioche.

("Finally I recalled the stopgap solution of a great princess who was told that the peasants had no bread, and who responded: "Let them eat brioche.")

Note that Marie would have been 9 at the time of this publication, and still in Austria. In fact, the attribution of the phrase to the Queen wouldn't even occur until after the Revolution was over and her head long severed. Its initial attribution to Marie Antoinette occurred in 1843 by Alphonse Karr, and subsequent historians have noted that such a statement would have been completely out of character for the ill-fated queen. From Antonia Frasier's Marie Antoinette: The Journey:

[Let them eat cake] was said 100 years before her by Marie-Thérèse, the wife of Louis XIV. It was a callous and ignorant statement and she, Marie Antoinette, was neither.

She was in fact quite the opposite, well known for giving generously to charities, and with deep concern for the plight of the poor - albeit, still a monarch in absolutist France, so she would only occasionally have such things brought to her attention.

As an interesting aside into my own field-of-choice, there's a similar phrase attributed to Emperor Hui of the 4th century Jin Dynasty in China. As per The Book of Jin, when alerted that the peasants were starving because there was no rice to be eaten, the out-of-touch emperor supposedly responded: "何不食肉糜?" ("Then why don't they just eat meat?") Unsurprisingly, he wound up assassinated about 6 years into his reign in 307.