No, wait, it was not "lingua franca in the educated western world", vulgar latin was just... the language a lot of Europe spoke for centuries.
People think of Latin as this highbrow educated thing, because that's what was left of it after the development of romance languages from vulgar Latin, but Latin was just what normal people used to talk to each other for a long time.
And yes, sure, texts on alchemy, mysticism and religion were written on it.
Also texts on food recipes, tax collection, how the tree from your neighbour's yard was blocking the sun to your oranges and the rude graffitti in the tables of the pub.
Honestly, I don't see why the chosen language would have to matter to your fictitious magic system. Surely if you have to say words and words mean things, the language doesn't affect what the words mean. I tend to like it when people still manage to tap into magical thinking without the crutch of pulling what they think sounds old-timey from somewhere. Neil Gaiman, Jim Henson or Grant Morrison were/are really good at it.
Or, you know, if you're a meganerd like Tolkien you can always just... make a whole new language for it. That also works.
Why are anglo writers obsessed with using latin as some ancient, mystical language? Why would Latin be tied to magic in any way? Do they realize that Latin was spoken all through Europe for millenia and its vulgar form evolved into tons of current languages? Or that people were using latin in churches, courtrooms and universtities all the way up to the 20th century? Latin was an optional in my high school. I took two years.
If random Latin words could do magic all of Europe would have been constantly exploding. Newspapers would be covering the latest magic volcano to pop up in Southern France. World War II movies would include accidental summonings.
Also, for us romance language speakers it sounds vaguely understandable, so the weird things they use for spells sound goofy as hell. I'm not sure if that's better or worse than using fake Latin-sounding made up stuff as in Harry Potter.
None of Star Wars makes any sense in context. From "Darth" to the whole I think I have your dad's lightsaber stashed here somewhere thing to who Luke's family is supposed to be and these days even Obi Wan's weird desert hermit outfit now being official Jedi uniform, apparently or how Vader keeps getting bullied by all of the Empire's middle management.
Honestly, that last one is the most impressive. In retrospect, Tarkin is an absolute badass that doesn't give a crap about Vader's whole deal. And it works. The magic space wizard that basically runs the empire and everybody is terrified of just sits there and takes it. You have to respect that.