Is there an expression in English for a thin old woman which corresponds to "Dry as a root" in French?
It doesn't explicitly refer to an old woman, but people (including myself) will often use the phrase "as skinny as a rake".
She's as skinny as a rake!
You could make reference to the woman's age if you wanted to by modifying the sentence to something like:
That old bag's as skinny as a rake!
"Old bag" is a slang term (sometimes considered derogatory) for an old woman; usually one with a bad temper.
It's not an expression, but a single word. Still, I think you can try decrepit
1.1 (Of a person) elderly and infirm:
a rather decrepit old woman