Sure, by the time Picard goes to school, thing may change, but due to the proximity of France to the UK, I think it will still make sense for European students to be taught in British English.
It's not that simple. There's already various regional accents in France and they're not close to English accents. A French person who's fluent in English will have an "international" accent with traits of his own French accent. Look, a lot of French people don't understand than "th" doen'st sound like s or z.
In English classes, they teach the "right"pronunciation, not an accent.
My sister's really fluent in English and she lives in Toronto, but despite we lear Canadian english, she still speak english with an accent. It's pretty noticeable when she talks with her boyfriend. His boyfriend only speaks English and grew up in Toronto, so when they talk together, it's easy to notice the difference.