While Madame Rue is in fact the casted name of the gypsy in A Ring by Spring, the gypsy in the Searchers song is Madame Ruth: rhymes with "tooth."
Caryn Briggs (Rachel Boston), the primary protagonist, wears eight different coats throughout the film. Most of her coats are of the pea variety with a limited solid color palate, including red, white, navy blue, blush rose, and black. This signifies the "basic" nature of Caryn's character.
Madame Rue is also the name of the gypsy who supplies "Love Potion #9" in the song by The Searchers
At 1:45 they shake hands through a car window. They reach with right hands, but the closeup of the handshake is left hands.