Why did the French soldiers in Paths of Glory cry at the end of the film when the German girl was singing?
The song evokes memories of their youth, their homes, and their loves in a world they may never see again. There is still a hint of their common humanity and sensitivity in the men despite the misery and depravity of war.
Quoting from this detailed analysis of the movie:
In the final memorable sequence of the film, Dax wanders in the streets of the town towards his quarters. He hears lecherous, cat-call whistling and shouting in a nearby tavern, where men from his troops are getting drunk for "a little diversion" (according to the master of ceremonies tavern keeper) following the execution. He stands outside in the doorway, witnessing the coaxing of a frightened, fragile, teary-eyed and innocent German blonde girl (Susanne Christian in the credits, actually Christiane Harlan, director Kubrick's future third and last wife). She may be a prisoner, or a refugee who is forced to sing a song in front of rowdy soldiers who are cat-calling, hooting, and laughing at her.
The girl is introduced by the tavern keeper as "our latest acquisition from the enemy...from Germany, the land of the Hun!" She is "a little pearl washed ashore by the tide of war" who has "a little natural talent" (he gestures over her physical curves) and "she can sing like a bird - she has a throat of gold." Dax recognizes companions of the executed men and is disappointed by their apparent lustful callousness shortly following the death of their own comrades. In front of the raucous troops, the timid and fragile young girl - with tears on her cheeks - begins to sing a ballad - in German. [It is a universally-known folk song of love in war, called "The Faithful Soldier" - (La Treue Hussar (Fr.) or Der treue Hussar (Ger.)).] It is a simple, sweet song that is inaudible until the audience quiets down and listens intently and respectfully to her plaintive voice. Soon, hers is the only voice in the tavern:
(the girls sings the song in German)
The soldiers - for once affected and showing some regard for human life - join her and hum along with their faces drawn to her. The human feelings in the song transcend the language barriers - some of the French soldiers may know the tune of their enemy's song, and some may even know the words. One of the youngest recruits in the audience has tears flowing down his cheeks. The song evokes memories of their youth, their homes, and their loves in a world they may never see again. There is still a hint of their common humanity and sensitivity in the men despite the misery and depravity of war.
Another beautiful explanation of the scene:
The song has begun to pacify the men, and so the frenetic pace of the editing slows as the gaze of the men moves from carnality to contemplation.
The men begin humming along at 2:25 as the young blond soldier swallows hard, as though preparing himself for something awful. The survey of faces continues, and the men look increasingly worried until the 2:42 mark, when an older soldier appears mortified, ashamed. At the 2:54 mark, we return to the young girl who has taken note of the men’s tears, and she regains her confidence, nodding her head to the audience to encourage them.
As the audience gazes at the helpless girl, the imagination of each soldier wanders off. The think of their wives, sisters and daughters. If a German girl could be plucked from her home and set before a room full of cat-calling brutes, the same could happen to a girl they knew. The young blond soldier weeps because the girl is not the enemy, but his own girlfriend, disgraced by jeers. She is no longer a German girl, but a girl, and then no longer a girl, but a human being among other human beings. The soldiers begin to cry not on behalf of the girl, but as the girl. Sympathy is an act of imitation, and every act of imitation is an act of becoming.