I am assuming the match is listed by Ancestry as paternal?
The suggested relationships by Ancestry are not worth paying much attention to. The pool of possible relationship can be quite large. But with the 30 year age gap and 686cM, 1C1R is most likely. So your friend's match is probably the cousin of her unknown father; meaning they would share a pair of grandparents.
What you will need to do from here is look at all the shared matches of this suggested 1C1R (using ProTools) and find out who the common ancestors are among them. You should be looking for other matches who share at least two more matches with the 1C1R in particular.
Some will have incomplete trees. Quickly open all the dead-end ancestors (with attention to ones in your relevant region), press to the search button at the top right of their profile, and find that person in public trees, or records. If you do this for all matches, you will probably find multiple matches with the same ancestors. This way you will be able to narrow down which side of the 1C1R's tree you relate to.
The relation is probably something like this:
| Shared great-grandparents (e 1890) | Shared grandparents (e 1890) |
| Unknown grandfather (e 1920) | Macth's father (e 1920) |
| Unknown father (e 1950) | Suggested 1C1R (e 1950) |
| Your friend (e 1980) | - |
But your friend has another unknown line, not shared with the 1C1R, so you'd need to go through your friend's matches listed as paternal and unknown, as briefly outlined above, starting with the closest matches. Though in about 5% of cases Ancestry gets the maternal or paternal side wrong. Find out how the matches are related, and note that down. Add a note to each one so you known who is accounted for and who is not.
Hopefully you will find close matches from your friend's other line. With the two rough lines known, you can then look for possible marriages between the line shared by the suggested 1C1R and the line he does not share. If you can do that you'll then have a list of possible sons, one of whom will be your friend's father.
If you can find both lines depends on how close the matches are, how many relatives you can establish common ancestors for, and how good you are at this research.
It's also possible your fiend's father was himself born out of wedlock, which will make it more complicated. Often DNA just gives clues and partial answers.
