Question

what had the narrator counted on to enter the school unnoticed

Answer 1

Quoted from Alphonse Daudet's “The Last Lesson”, a little tyke named Franz (narrator) being self-restrained from the thoughts of his own started up for his school to enter into the class unnoticed.  

The reason behind this unnoticeable entry would be the dread and terror of scolding he was about to receive from Mr Hamel (his teacher) for not learning 'Participles' and for arriving late at school.  

He was thinking of the tensing atmosphere and the noise of the rapping ruler, rattling sound of desks and the voice of the students repeating the lessons which can be heard miles away from the classroom.  

Franz (narrator) counted on this to enter the class unnoticed to escape from his punishment from Mr Hamel.