Since "to have" has various translations in Japanese, I think it has more difficulties than "happen to" in this case. Besides, in many cases, the literal translation doesn't work nor sound natural, so we have to change something depending on the context. Anyway, "happen to" mainly means ぐうぜん … する、たまたま … する. Anyway, I would translate: "I don't happen to have any foreign friends" 私にはぐうぜん外国の人と友だちになることがない。 (It's like "I don't (have oppotunity to) happen to become friends with foreign people".) "I happened to know her phone number" 私はぐうぜん or たまたま彼女の電話番号を知った。 (It's like "I happened to know her phone number".) *I wrote in the informal form in Japanese. If you need how to read kanji or more explanation about them, please let me know. I hope this helps you.

Ryoko-san's answer is not necessarily wrong. It's just that she doesn't seem to know the nuance of "happen to...", so allow me to show you another way to say this. You can use the word: "心当たり" (kokoro atari). For instance, if you want to say: "I happen to know her phone number", you can say: "彼女の電話番号なら、心当たりがあるんだけど”. If you want it to be more polite, you can say: "......あるんですが” But if you want to say: "I don't have any foreign friends", kokoro atari is not a good choice in that case, you probably want to follow what Ryoko-san wrote. However, in my opinion, in Japanese, people don't usually say "happen to...". In a casual situation, one would simply likely to say something like: "あ、俺、彼女の電話番号を知ってるんだけど” ”俺、海外の友達がいない” PS: You probably shouldn't learn a language by translating a sentence to another, especially when it comes to two completely different languages like Japanese and English.

When I was asked " Do you happen to know his address?" from a native English speaker who is my boss, I feel there is roundabout and politeness. so, こころあたり　is right. On the other hand, "I don't happen to have any foreign friends" is a little different from こころあたり。so you could say, がいこくじん　と　ともだちに　なることがない。まだ、ともだちが　いない。　also, I think if you want to say " I want to make friends, but I don't happen to do." ともだちに　なりたいが、きっかけが　ない。きっかけ＝oppotunities. One more thing, "happen to ~" is translated to "たまたま/ぐうぜん～する”　This is a very common words. そこに医者が、たまたま/ぐうぜん、居合わせた。 A doctor happend to be there. I think the answers of Ryoko and Rey, both make sense. Pleases remember various meanings. I hope this helps.