As an avid Beauty & the Beast lover (I loved the live-action so much, I don't even care that the French country people have adopted British accents!) I would love to tackle this question! Note: I've watched the live-action version like... 8 times recently and it's been a while since I've seen the cartoon, so I might include something that isn't 'canon' in the original!
There is actually a lot to be said here that I think is super interesting! It's definitely not a tale as old as time of "man = learning" "women = no learning", and also gives us a unique insight into one of the reasons the Estates General/National Assembly will go poorly for the nobility!
I'm going to take some liberties here, founded on educated guesses, and say that Gaston was likely a provincial noble, given his leadership role in the community and his hinted at high position in the army, along with his haughty demeanor and hangers-on.
Provincial nobles are distinguished by normally having more ancient lineages than the more recently ennobled "robe nobles" who had purchased a venal office-- one sold by the king to make dat money. These older nobles, referred to as "sword nobles", looked down upon these upstarts as not real nobility, and were generally jealous of their wealth. Many provincial sword nobles, like Gaston seems to be, didn't have the large fortunes of either the robe nobles or the major courtiers who lived in Paris and Versailles. Gaston likely lived on his provincial estate, still much wealthier than the peasants, but perhaps not much more so than the wealthiest townspeople (bourgeois).
The army was the one place where sword nobles still held a lockdown on jobs. In 1781 the Ségur Ordinances decreed that a noble family had to have their nobility go back at least four generations to be considered for top positions (I go much more in depth on this here.), so Gaston would likely have been brought up in the military, as that was the last bastion of honor for his family to show that they were better than others, and where he'd have had the most opportunity.
So why does this matter? Well it just so happens that we have many letters from noblemen just like Gaston who were elected delegates to the Estates General in 1789. In these letters, we see them complain at length about the paucity of their education compared to the Third Estate delegates (middle to upper middle class men).^(1) Many of these men were sent off to the army as children-- some as young as twelve-- where their focus was far more on discipline, honor codes, weaponry, and military procedures, with little to no education past what was required to perform these tasks. Many of these men retired from the army at what we would consider a young age (30s-40s), so Gaston being back in the Town is not out of place here. Given his value system and his importance on martial virtues it seems likely that he was shipped off to the army at quite a young age and brought up as an officer. After all, no one fights like Gaston.
Back to our noble delegates to the assembly, we see in many letters that those who had been in the army (a great many, especially among our provincial nobles) were incredibly frustrated that they were not educated, and therefore were unable to go toe-to-toe with the delegates of the Third Estate-- men who were predominantly involved with the legal professions in some way, and therefore were educated extensively in oratory, and had read widely. From the pen of one noble delegate, an army veteran named Archard de Bonvouloir, "My ideas are often sound and broadly conceived, but for lack of education, I have difficulty developing them." Another noble delegate lamented the lack of education of noble officers, stating that their "childhood formation is generally neglected," and that they, "enter military service without education and leave without ever having acquired any."^(2) It is therefore likely that Gaston too lacked an education. While many of our noble delegates in the Estates General hired tutors, hoping to make up for lost time, learning something there that wasn't there before, I think we can agree that our Gaston saw no benefit in the delicate pursuit of 'knowledge'. He knew what he owed to the Church and the King, he knew where he stood in the hierarchy (above the townspeople), and he knew how to defend his Honor, by strength if necessary-- books were useless pieces of paper, only good for ripping to demonstrate bicep strength. Therefore I think we can conclude that, while Gaston likely knew how to read, this was the furthest extent in his non-militaristic education. It's even plausible that, since returning from war, Gaston has made no business of reading whatsoever, and his learning might perhaps atrophy over time, instead depending on his more educated servants to take up this task for him.
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