The correct option is
C She
Option A: 'She' refers to the "poor young girl" mentioned in the passage. It completes the given sentence in meaning: the poor young girl came across a gentleman to whom she narrated her story.
Hence option A is correct.
Option B: 'There' is used to introduce a clause when there is no other subject.
'Across' means 'to come into contact with'. The word 'there' does not relate to the given sentence because of the word 'across'. 'Across' needs a personal pronoun to establish its meaning of 'coming into contact with': 'she' came in contact with the gentleman, as opposed to 'there'.
Option C: 'He' refers to a boy whereas the passage speaks about a girl.
Option D: Similarly, 'they' refer to people, whereas the passage speaks about one person, a girl.
Hence options B, C and D are incorrect.