Lol - was lovesick fashionable in these times? Or was it a question of "rhythm"?
Well, the verb "tanner" has several meanings:
(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