Dear Sarah - Have just found your post. I had not heard the story of the Scottish linkage before! I had always supposed that the name change occured in the 1600s, when French workers were brought in to do the red tile roofs in Yorkshire.
Looks like our linkage is through our common great Grandfather (Walter). My Mother was Mabel France, daughter of Rowland Ellis France (1889-1934) and his wife Mary Ida (1891-1967) who lived at Ravenscar, where I spent many summer holidays. Rowland was the brother of your Grandfather Harold, so I guess your father and my mother were cousins.
Thanks for the information re the connection with the James France Mill as we did not have any solid record on this, ecept for an online photo of the company cricket club.
I moved to Canada in 1969, but there still seems to be masses of Frances in and around Ravenscar. My 4 brothers and one sister (Longs) still live in England. If you want any further info please contact me at email@example.com