It's more than a chance he told her the whole story as part of a jealous row.
As to the woman being French, I infer that from the note.

She couldn't trust her English or she would not have written in French.

That note, being in French, would narrow any search for its author; and that, too, whether the author were English or French.

Certainly there are fewer people in Washington who can write French than English.

You see the point ?" "But you said a Frenchwoman from Ottawa." "The note is on paper that was made and sold in Ottawa, as you see by the raised mark in the corner.