So here's my knee-jerk attitude:
To the modern non-French speaker with a brief understanding of language evolution, the Académie sounds like something that is ill-conceived, arrogant and doomed to stagnate thought and culture in an attempt to keep France in the 17th century. Languages don't work like the Académie is designed to maintain, and this simple fact will ultimately lead to its irrelevance. Which means that the continued existence of the body seems pointless.
As an Anglophone, there's a certain sense of superiority we feel in that we're basically able to go pretty much anywhere and find somebody who speaks passable English and we don't have an equivalent body. Whenever the Académie comes up in the Anglosphere, it's in the context of an attempt to prevent an English word or phrase from officially entering the language, even though (and this is the attitude) "any stupid person can see that English won out and why not just let the loan-words in".
So that's my knee-jerk attitude, being entirely honest.
However, there's a deep rooted insecurity that's built into many English speakers. The paradox and complexity in the attitude is that English is basically a language of mostly loan words. And due to history, we inherited various modes of the language that represent various social class structures...one of the oldest was the split between the Germanic roots of English and the French (Norman) roots of English in the 11th century. To this day, the Latin or French root words are considered "superior" to the Germanic or Old-English equivalents. In some cases, the Germanic roots are considered "forbidden" while the upper-mode equivalents are considered okay to say in perfectly polite conversation. For example, "fuck" and "fornicate". This insecurity, and the modern global dominance of English (which happily uses "lingua franca" to describe itself) means internet posts about the Académie are bound to make fun of it.
But I think it also stems from not understanding in any way the historic reasons such a body was formed, maintained, and then reinstated when it was abolished during the revolution. It's virtually incomprehensible to the modern Anglophone to understand that France in the 17th century had such a diverse linguistic landscape that travel from one village to another meant needing a translator.
This post on /r/AskHistorians was incredibly enlightening to me and has completely turned around many of my earlier feelings about the Académie: https://www.reddit.com/r/AskHistorians/comments/7u8oyk/how_t...
That thread is full of incredible information that I was almost entirely ignorant of and as I read the various follow ups, especially the ones about Napoleon, I realized how important a unified language was for military and economic matters.
From the link "As late as 1863, "a quarter of all army recruits were said to speak 'patois' and nothing else," Robb writes.
This often didn't last long. There are many reports of soldiers learning French while in military service, because of the necessity of communication and orders.
But "men returning from the army quickly reverted to their native tongue. A man who came home to Cellefrouin near Angoulême in 1850 after seven years in the army and thirty years in America was speaking the patois of his boyhood again within a few days."
This wasn't a universal case, however. McPhee notes the young men of Mazières who came back home from military service in the 1870s "determined, as a sign of their worldliness, no longer to speak patois" (220).
As late as 1914, "there are several reports of Breton soldiers being shot by their comrades in the First World War because they were mistaken for Germans or because they failed to obey incomprehensible orders.""