The term, melodie, refers to French songs of the 19th and 20th centuries, usually, but not always, for solo voice and piano. It is the French equivalent of the German “lied” or the English art-song. It is a product of the Romantic era and most major French composers, from Hector Berlioz in the 1830s to Francis Poulenc in the mid 20th century, have contributed to the treasury of the form.
The form became more distinctively French as it went on, especially from Debussy on with the works of the great French poets being the recipients of most of the settings. Like all true art-songs a great deal of the charm, indeed of the “art” itself, lay in the sympathetic partnership of the voice and accompaniment.
The most prodigious of the writers of melodies (and one of the most popular [1]) was Gabriel Faure who wrote well over 100 of them. One composer, Henri Duparc, is known solely for his melodie compositions.
References:
“Oxford Companion to Music”
“The Grove Concise Dictionary of Music”