If the purpose had been to be better at taking notes with pen and paper, than being taught to write in shorthand would have been a much more useful skill than being taught to write in cursive.
It's not taught, but it is a skill one also develops. Probably this is not taught because french kids already have a hard time with spelling.
Fun fact: french physicians are well known for undecipherable cursive hand writing. Part of what makes it difficult to write is that they use Greek letters for short hand. For instance, they replace "-tion" suffixes with a theta, or the "ph" combo with a phi.
Shorthand tends to be somewhat difficult to read quickly, difficult to scan, and somewhat personal to the individual stenographer. To make the notes useful most people would need to transcribe them first.
