I don't know of any specific term. Why, these are just average American schools. ;-)
On a more serious note, the only thing that might come close is "inner city school". While there is no reason that an "inner city school" couldn't be a model of classroom learning with eager, bright, motivated students, it is usually associated with schools that have the same problems as Brennpunktschulen, ie., large portions of the students in class that don't speak German/English, parents that don't care much about their children's education or are just not there, rampant drug use, violence, gangs, etc.
Und jetzt habe ich eine brennende Frage und zwar: Könnte eine Brennpunktschule auch in einem Dorf sein? Auf dem Lande?