Lol - was lovesick fashionable in these times? Or was it a question of "rhythm"?
Well, the verb "tanner" has several meanings:
http://dictionnaire.reverso.net/francais-anglais/tanner
(did they forget to mention "beating", "battering"?)
and the old French expression "tanné d'amour" has gone lost, except for the Québec.
In our times, they refer to "malade", i.e. "sick":
Lara Fabian interpreting an old tragical song with subtitles (FR, EN):
(you might have heard of Dalida (the song told about her own tragedy), Serge Lama (writer and also interpreter) and many other great singers, who interpreted this song)
or - much more positive:
Michel Sardou - La maladie d'amour (The Disease of Love)
(lyrics with English version) - http://lyricstranslate.com/en/la-maladie-d039-amour-love-disease.html