I think "libérée" could work, or also "libre". C'est une femme libérée
or elle est très libre.
[Of course I assume you're talking about women, since men with a very free love life are just womanizers whereas women with a very free love life are slutty... ]
"Libertine" has different implications. In the 18th century, "un libertin" (a libertine or a rake such as Lovelace in Clarissa or Valmont in Les Liaisons Dangereuses) was someone who opposed religion and morals and who usually had a wild sex life as a result.
If you say of a woman, nowadays, she's "une libertine" you mean she likes sex and has a fancy sex life whereas if you say she's "libre" ou "libérée" you rather mean that she does'nt believe in old-fashioned morals and behaves accordingly. So that's pretty different : you can be "libre/libérée" without being "libertine".
"Je-je suis libertine (-> I'm a libertine)
je suis une catin" (-> I'm a harlot)
Mylène Farmer used to sing...