By coincidence, I have something very similar in my ancestry. My mother's mother's father was born of such a union. The only clue I have to the father is a newspaper photo. The photo is captioned as by the famous celebrity photographer Count Jean de Streleki but no name of the subject is given, and since the text is missing, the article may have been about the photographer rather than my gg-grandfather. I can't even tell what newspaper the article is from, although it may be a New York newspaper. Someone has written "Gustav Rosell was his illegitimate son" on the edge of the photo and my mother or one of her brothers has written "Gustav Rosell's father; mother's grandfather."
If anyone recognizes this guy, I'd be happy to know who he is. I believe he might be German, but could be Swedish as were all the rest of my mother's family. Gustav was born in 1852, so this guy would have likely been 20-40 years older than that. (I have googled the text on the back of the photo, hoping to discover it in some newspaper archive, which would then let me recover the text of the article surrounding this photo, but no luck so far.)
At any rate,
dna testing (autosomal, since in both our cases the line is mixed male and female) could possibly give us clues as to the general family connection of our mysterious (and libidinous, and likely wealthy) ancestors. It would take a LOT of luck to make the actual connections. This is especially true since Europe has much stricter privacy laws than the US. But if someone should show up in our suggested "4th to distant cousin" matches that would otherwise fit the description, it might just be worth checking out. Yours, at g-grandfather distance (as opposed to mine at gg-grandfather separation) would be a lot likelier discovery.