I think you mean-If you offended a foreigner friend, how do you tell him that you are sorry? You should tell them the truth. If you didn't fully understand what you were saying due to your lack of English knowledge for example.

I feel as though when__________(I said or this happened) I might have offended you. If I did, I just want you to know that it was a part of a miscommunication. I am so sorry. Let me explain what (happened or what I was thinking at the time)....Explain..... I hope you understand. Thank you for listening, it was nice to get that off my chest, even if it did not really bother you. I feel better after explaining that."

If you have genuinely offended someone, the best you can do is simply apologize and acknowledge your wrongdoing. If your friend was offended due to a miscommunication, tell them 误会！

Tell him (probably a him I'd take) a bonus from you. That solves every problem.

I think Chinese people generally apologize too often :) but if you feel that you should apologize, you could say something among the lines of: - I'm sorry, I didn't mean it like that. - It wasn't my intention to offend you. - No offence, but...