Is merely repenting to Allah the Almighty sufficient for falsely accusing a non-Muslim of theft, or is it obligatory to apologize to him personally despite fearing legal repercussions?

It is not permissible to accuse anyone of theft except with clear evidence or strong circumstantial indicators, such as fingerprints and video recordings. Otherwise, it would be a false accusation. The general rule is the obligation to seek forgiveness for an injustice. However, if apologizing would lead to a greater harm, such as being compelled to pay compensation, then seeking forgiveness is not obligatory. In such a case, repentance suffices, along with publicizing his innocence in the places where he was accused. Compensation for emotional damages is not legislated.