What is the ruling on slandering the people of a country with an unconfirmed story about invaders raping their free women, given the slanderer's repentance?

Your statement that "the invaders raped the women of the land" is not a slander (qadhf) that necessitates the legal punishment (hadd), but rather a sin that requires discretionary punishment (ta'zir). This is because whoever accuses a chaste woman of zina (unlawful sexual intercourse) under duress is not subject to the hadd punishment; rather, the ruler will administer a ta'zir. If you repent to Allah with a sincere repentance, then part of the completeness of this repentance is to seek forgiveness from those you shamed and to rectify the error by informing those you told that you said it without proof, unless doing so would further spread the news and its corruption. In that case, you suffice with repentance between yourself and Allah.