Getting a satisfactory definition of it has been a decade-long treasure hunt without a map, then translating it is something else. I am thankful for the hyper-xenophilic absorbency of the English language: it turns out 缘份 is just "yuanfen", as "Schadenfreude" is just "schadenfreude" and "amok" is just "amok"!
I have only come across this in Japanese (縁) and had assumed that it would be in Korean (I do not know Korean at all) too. Yet, using cloud and paper dictionaries, I invariably end up with 인연, then flipped 인연 back to Chinese and Japanese, the result is 運命 (fate or perhaps destiny), not at all the same notion. I tried Nepalese and Thai, very similar outcomes, given that the concept was Buddhist.
In fact, in Chinese, there is this nuanced concept which distinguishes the meanings of 缘 and 份 which gets even more complicated and frustrating for translating: 缘 may not be fulfilled due to the absence of 份, and 份 can be coerced but for that to happen 缘 had to be there in the first place, else there would be no encounter.
Separately, are there any other non-Asian languages that have their versions of 缘份, perhaps independently?
So far, none of the European languages go beyond "fate" or "destiny".
I would very much appreciate any input on this.
As a Chinese, I can help you a little
Here's an explanation and a hypothetical situation that can help you with the Chinese words "缘分" and "缘份"
"缘分" is the meaning of "fate", only one level of meaning, is not looking for results of a kind. For example, if old classmates meet again after decades, this is called "fate".
"缘份" has two meanings, is in the "edge (fate)" on the basis of, but also can seek the results of a kind of. For example: the man and woman met, can be married, called "fate" to; parted in the middle, called "fate" has not yet arrived, or called "fate without a part.
But in use, we are used to writing the latter as the former as well, and it is time to understand the meaning from the context
Sadly, I don't know any word that is equivalent to 缘份 in non-asian language, so maybe you have to retell Chinese with other language based on context, rather than find a one-to-one translation... But as a Chinese, maybe I can tell my feeling about the word 缘份. It has two distinct usage. Generally, it means very good and precious relationship of coincidence, and it is kind of explained in Chinese superstitiously. Maybe its origin is from Buddhism.
The first one is that, if two person happens to be with each other accidentally for a lot of times with no reason, we can describe them with 他们之间很有缘分. For instance, two students in the same class in their high school went to different college. Without any communication, they happens to apply to the same graduate school and the same lab! Another example is that two co-workers happens to be good friends in an online forum, like cooking Indian food, without realizing the identity behind the screen of that neitizen's for a long time. They are appropriate scenarios to be described as 他们之间很有缘分.
The other meaning is that two people that PERFECTLY fits with each other in personality, character, hobby, understanding towards things, etc. and meet with each other, and then deeply communicate and support each other.You can't use 缘分 to describe common good relationship, but only the relationship that is very precious. Usually, that kind of relation may happen to someone only once in their life. You can sometimes describe that kind of friend as 知己。
Hope that its' helpful to you:)