Using ancestry.com family tree hints, I also seem to go back to George Fane and Sir Francis Fane. Ancestry.com suggests that George Fane was the son of Sir Francis Fane.
You might want to take a look at my tree to see if we share any common ancestors.
However, I'm not sure if George Finn/Sir Frances Fane are are actually ancestors of mine. I think I've gone wrong somewhere, and will need to look at source documents. I'm fairly confident in my line until around 1820 in the Chilham/Canterbury, Kent area of England.
The story I've heard and seen in a number of diaries is that those Finns moved from Northern Ireland to Kent suddenly, and it must be within the living memory of a few generations so I wouldn't think that story would be older than the 19th century. The Finns in my tree had been horse trainers in Northern Ireland. They were originally from Finland, and continued to trade with Finland after moving to Northern Ireland. They changed their name from Godolphus to Finn in Northern Ireland, and later moved to Chilham, Kent (around the Canterbury area). However, it's early days yet! None of this has been confirmed, but let me know if you have anything similar in your tree.
So while Ancestry.com is telling me that George Fane and Sir Francis Fane are ancestors of mine as well, I'm taking it with a grain of salt.