And now she was sure that Adele was the name used.

I remembered her hesitation when I read Marthe Gobin's letter.
They helped to confirm me in my theory that she was in the plot; and they made me very sure that it was an Adele for whom we had to look.

So far well.

But other statements in the letter puzzled me.

For instance, 'She ran lightly and quickly across the pavement into the house, as though she were afraid to be seen.' Those were the words, and the woman was obviously honest.