Dear Brummies: Thank you all for your advice and information. I have spent the day working your ideas. I pursued Carolina's idea of the Sarah France in Leebotwood. I have a subscription to findmypast.com, so I checked the details. There is a whole family of Frances, parents Isaac and Hannah. The Sarah France birthyear (1811) works perfectly. However, Leebotwood is about 25 miles from Coal Pit Bank(aka Ketley Bank). So it stretches credibility a bit. But I found two of the children had their surnames listed as Francis rather than France and that got me thinking.
I checked Wombridge births for Sarah Francis and I found one in 1809 to Thomas and Mary Francis with a brother James, born in 1805. This is the parish where I think Coal Pit Bank was (just a mile or two away).
Here is the problem: None of the names of the siblings in either family match any of those of Sarah France Appleby's children or the grandchildren I know of.
So I am still not convinced I have the right folks.
But I sure appreciate all your help. I still remember fondly my visit to Birmingham a few years ago and hours spent in the genealogical records office. Thanks, again.
Cliff, the Ontarian.
PS: I am willing to do a few findmypast.com lookups for others.