How can one atone for the sin of fornication with a Christian girl who refuses to embrace Islam, and whose family refuses her marriage on the pretext of her young age?

You erred in your relationship with a woman unlawful to you, in your travel to an infidel country for her sake, and in your living with her and her family. The greatest of these errors is committing adultery with her. Islam has forbidden adultery most strongly, as Allah Almighty says: "And do not approach unlawful sexual intercourse. Indeed, it is ever an indecency and is evil as a way" [Al-Isra 17:32], and as the Prophet, peace and blessings be upon him, said: "The adulterer does not commit adultery while he is a believer."