Sorry, that sounds horrible. I'm a teacher and before moving to France I taught 6th grade at a French school--I was the homeroom teacher. I was used to high school and so shocked to find out how mean younger kids can be--and how it really can affect the kids who are being picked on (and frankly even the bullies who get a little backlash end up feeling terrible and stressed out). It's a bad situation for everyone.
I noticed--in my opinion that culturally the French teachers were somewhat more lax about bullying (and perhaps French parents too). There was a kind of 'deal with it yourself' attitude. One teacher even told a girl who was being bullied to 'just be mean' back.
Regardless, it's frankly quite hard to deal with as a teacher because sometimes you'll get the bully not being honest about what they did--obviously--but you didn't see it happen. . .again hard to handle even for a veteran teacher but a newbie with a class out of control is going to have far more problems.
I'd say first try to get your daughter to face it as their problem not her problem, which I know is hard to do, but it's important she see that they're the ones being petty and obnoxious and that there are always people like that out there who are ready to pick on someone for--whatever. And probably in junior high the bully will get picked on etc. I think no one is spared.
Is the director of the school decent--or do you know any of the more experienced teachers? They might be able to give you some advice or the new teacher some advice--also, all of the teachers are around during recess time. My husband is a primary school teacher and he has started working with a problematic student who he will have next year just to give him some stability (not your daughter's same situation, but still, her own teacher is not the only resource you have.)
If you can establish that the girls' parents are reasonable people, maybe trying to contact them would work--but if they're a little crazy that can backfire--you have to be the judge of that. Maybe other parents of kids that can be there for your daughter could also be an asset. You know, so you don't get others just going with the flow of the bully. Maybe help foster a few really good relationships with some kids in her class--or in a class close in age group.
Dunno about how useful the inspection could actually be, but they can be known to at least attempt to put pressure on the teachers, so as a last resort, it might be something to try. You might also want to mention your concerns about the new teacher and the discipline issues. Maybe she seriously needs help.
Good luck! I feel for you. My daughter is only three but I dread the thought of helping her face bullies. . .