Comics

What’s wrong with je mange, il mange, ils mange‽

Nothing in theory, but my native ass recoiled in horror at "ils mange". I know it's literally equivalent and I shouldn't care, but French is culturally very attached to its written form, even moreso than English (the reasons why being outlined at the end of my comment).

But yeah, I thought that apart from the passé simple my examples were pretty standard. Is that not so?

In the written form, yes. In the oral form, it depends. Futur proche has evolved to be used quite generally.

• Je mangerai: Can be rather formal? Not unusual but I'm more likely to say "ce soir je vais (j'vais) manger une salade" than "ce soir je mangerai une salade". Or in an email I will say "je verrai ça avec X" but on the phone I'll say "je vais voir ça avec X". I think the comparison to will vs going to is adequate, the main difference is that going to uses too many syllables; I'd say futur proche has the ease-of-use of "gonna" but the somewhat formal connotation of "going to".
• Je mangerais / ils mangeraient / vous mangerez: Basically the same thing but with "j'aurais mangé / ils auraient mangé / vous allez manger" as the thing I'd be most likely to say orally.

French conjugation is incredibly complex by any standard, and especially compared to English. There are tenses (e.g. imparfait du subjonctif) that are so archaic they're a complete meme and they shouldn't be used even in the most formal literary setting.
Sarkozy (well-known for being a feisty classist right-wing money-laundering asshole) using it as an obvious flex made the news at the time and everyone made fun of him. To this day I'm not even sure if he actually conjugated that correctly (and neither are the people in the comments lmao). That video is absolute gold, the eyebrow raise he does as if to say "and there" tells you everything you need to know about his character.

That is fun! My favourite fun French dialect fact is about septante, nonante, and huitante/octante being used in Swiss French and maybe Belgian and non-Quebec Canadian French instead of soixante-dix, quatre-vingt-dix, and quatre-vingt. I’m not sure of the history there, but I like it.

The Celts! No, seriously. They used a vigidecimal (base 20) system and since they counted in "twenties", "four twenties" is an artifact of that. So are 'single digit' numbers up to 20 (quatorze/quinze/etc). In that way "Quatre-ving-quatorze" is arguably correct base-20, but "quatre-ving-dix-huit" is not (because there is no dedicated number for 18 anymore so the whole thing is clunky, but "quatre-ving huitorze" would be fine conceptually).
I wonder if the germanic "eleven/twelve" is related or if it's an equivalent but unrelated evolution for counting scores.

Regarding the history of the language and its lack of reform, I am not a specialist but this guy and his colleagues are (if you're willing to go through half an hour of French with admittedly very good auto-generated English captions). But generally the idea is that the Académie and the system which created it have worked together since the early 19th century (which not uncoincidentally had the last major reform of the French language) to turn language into a very strong marker of social status. Like, very.

French people (and esp. Parisians) have a reputation for being assholes who will get mad at foreigners for mispronouncing words or using the wrong grammatical gender. That's asshole behavior but there are assholes everywhere, so why the French in particular? Because the French are taught from the age of 5 that their mastery of the French language (both written and spoken) will be the main thing for which they will be judged in life. As the middle class rose in the 19th/early 20th century, they got access to more/longer education where grammar/spelling was very heavily emphasized. Proper grammar/spelling then became a huge indicator of a good education and predictor of social mobility.
This fundamentally classist idea persisted well beyond the industrial revolution and it remains a very big talking point. "Young people can't write anymore" is probably the most common/recurring moral panic, and the idea that children age 6-12 should do mandatory daily (!!) graded spelling bees again is a regular conservative talking point because that's how they grew up (and it's still the policy with more... catholic-conservative teachers, I had some of those).
We don't usually even have spelling bee competitions (in all my schooling there was only ever one that I knew of), because stellar spelling is the expectation, not the over-achievement.
I'm sure that happens to a lesser degrees for English speakers, but now consider how much harder French is to write. I hope I got across how incredibly neurotic the French are over these matters.