I don't think it's worth too much, for the following reasons:
10k is just a step up from costume jewelry. Expensive stones aren't generally set in it.
The center stone, olive/dark green color isn't in high demand, and it doesn't appear to be cut all that well, which also point to it not being an expensive stone. If I had to guess, I'd say it might be a lower grade peridot, tourmaline, green zircon or a simulated stone.
The diamonds, if that's what they are, appear dark, also not high quality.
None of which means it can't be a lovely ring to wear and enjoy or have sentimental meaning, of course. Pricescope mostly deals with rather expensive jewelry so can be a little snobby lol.
The "FP" is probably the maker's/company's mark imo. I googled it and from what random people on the internet said, it could also mean "finished product" or that it has a hollow core, though I'm not sure how "FP" would stand for that.
You could go on ebay and key in something like "vintage 10k green stone ring," then scroll down and, on the column on the left side under "Show Only" click on "sold items." Then look over the listings to see what similar items have sold for.