[Re-Description] Bittersweet

Reading Anne Carson's Wikipedia page,

Eros the Bittersweet – Carson's first book of criticism, published in 1986 – examines eros as a simultaneous experience of pleasure and pain best exemplified by "glukupikron", a word of Sappho's creation and the "bittersweet" of the book's title. It considers how triangulations of desire appear in the writings of Sappho, ancient Greek novelists, and Plato. A reworking of her 1981 doctoral thesis Odi et Amo Ergo Sum ("I Hate and I Love, Therefore I Am"), Eros the Bittersweet "laid the groundwork for her subsequent publications, […] formulating the ideas on desire that would come to dominate her poetic output", and establishing her "style of patterning her writings after classical Greek literature"

In Eros the Bittersweet, (Amazon) Carson writes:

It was Sappho who first called eros “bittersweet.” No one who has been in love disputes her. What does the word mean?

As I read this, something occurred to me: Perhaps the word bittersweet is an English word that could hang with the French word jouissance?

I imagine myself suggesting this to a group of Lacanians... I'm not sure how they would respond to this.