This is a story, to some degree, about just that--romantic love. Even the title, The Awakening, is suggestive of this theme. Clearly there is more to Edna's "awakening" than simply falling in love; however, it is a new kind of love which spurs many of her actions and reactions throughout the story.
Edna married young and for all the wrong reasons. She had children, as well, and the family unit was the complete picture of a typical family in that day and time. Her relationship with Robert starts as a friendship, moves to a flirtation, then begins to take root and grow strong. While Edna is still in the midst of knowing her own mind and figuring out whether she cares enough to flaunt the rules of society, Robert has left. It's simply too painful for him to be around her and not with her.
It takes a while, but soon we see a changed and more independent Edna, crying on the sofa as Madamoiselle Reisz plays her a Chopin Impromptu, with a crumpled letter from Robert (which is not written to her) in her hand. Their eventual reunion is bittersweet, and they do eventually get to express their love for one another. All to no avail, of course, as Edna ends her life shortly afterward.
The view, then, of romantic love as seen in this work is that it is rare and painful and lethal if it happens between two people who can not be together.