The feeling in Frantz's classroom is

The feeling in the classroom is dejected and mourning.

Explanation:

Franz in the classroom of the Last Lesson is giving his last lecture of French before the German forces would take him away and make the study of the mother tongue of the children illegal.

Thus his last lesson is in a sense the last part of the life of those children apparently for them when they will be one with their own culture and then from thereon a foreign language will be imposed on them.

This is why the room is somber and dejected in the narrative.