The following translations are from online French and Latin dictionaries:
FRENCH:
Beautiful: esthetique, belle, beau
Woman: femme
Beautiful Woman: jolie femme
Song: chanson, chant
Happiness: felicite, bonheur
LATIN:
Beautiful: bellus, decorus, formosus, pulcher
Woman: femina, mulier
Song: camena, carmen
Happiness: beatitas, felicitas, gaudium, laetificus
A lot of names come from or have been influenced by these Latin roots (
Bella,
Felicity /
Felicia,
Carmen,
Beatrix and
Laetitia, to name a few) but
Caroline clearly does not.
I'm afraid your alternative meanings for
Caroline are no more than wishful thinking.