Final answer:
Count de Guiche believes Roxane loves him due to her passionate reaction to his announcement of going to war.
Step-by-step explanation:
When Count de Guiche thinks that he "loves him a little", it is due to Roxane's reaction to his announcement of going to war. There is evidence in classic literature of characters being swayed to believe in a romantic interest's affection following a significant event or revelation. In the case of de Guiche, Roxane's intense reaction, combined with her passionate statements about the glory of war, makes him sense a personal connection and possibly misconstrues it as a sign of her romantic interest. This interpersonal dynamic is a common theme in literature, where characters interpret actions or words as indications of love, sometimes mistakenly.