For me it was from introversion (which I understand may go along with perfectionism - at some point the line starts to blur).
So, if your dd is experiencing anything like I was, the last thing I'd suggest would be to force it. As a practical matter, a little "I'm sorry, I didn't hear you dear, can you speak up?" is about as far as I would go in a group scenario. (Perhaps the embarrassment of being called out on the quiet speaking is enough to encourage her to get it loud enough on the first try next time.)
that's my two cents on low speaking in school
I always thought of DD as extroverted.... maybe I should reconsider it (for this and for another reasons).
Anyway, your approach is what the teacher does. She is really kind and would never do something as horrible as they did to you. She asked me to tell DD 'sorry dear, could you repeat this? I did not hear you well' in order to encourage her to speak louder. This is when I realized that she does speak very low only at the school.
About the foreign language, well, outside the school she does not have any problem speaking with friends in her play-dates (in Dutch). Although maybe she fears to be corrected by the teacher, mmmm....
