Ancestors of Smith Schmitt from Alsace Lorraine France

My great mother was Jacobina "Bena" Smith (1840-1925) from Illinois.
Her father was Christian Schmitt (1800-1876) and her grandfather was
also Christian Schmitt (1767-1801.
I cannot go back further in France or better yet, Sumiswale, Switzerland.
Can anyone help.
Thanks,
R W Summers