What is the main conflict in A Very Long Engagement by Sebastien Japrisot?

When Mathilde Donnay’s fiancé is reported killed in action, she begins a quest to find him and four other soldiers who have been abandoned by their own army. Although Mathilde cannot walk, she can fend for herself, and she is intelligent and resourceful. Through interviews, letters, telegrams, and visits to important places Mathilde gathers information that leads her to discover the whereabouts of her lover, Manech. The reader must follow the clues as Mathilde does in order to find out what has happened between Saturday evening and Monday morning in January of 1917.