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.