If all you want to do is set the text of the label on the frame to red then, my thought is to do some thing like this.
Gtk::Label * frame_label = dynamic_cast<Gtk::Label *>(frame_widget.get_label_widget());
frame_label->set_markup("<span foreground="red">Red Text</span>");
Note that I have not tested this
As an additional note do not depend on the colour of an object to give all the feedback to the user. In this case the user may have colour blindness which affects red so would not see any visible change.