First of all, I should say this rec is not about the movie Blue is the warmest colour (orig. Le bleu est une couleur chaude), which I haven't seen -- but which is, or at least that's my impression, very very different from the graphic novel it's based on. So the graphic novel by Julie Maroh is what I'm reccing here.
Clémentine (for some reason renamed "Adèle" in the movie) is a fairly ordinary teenager who one day passes a blue-haired girl on the street, a girl she's incapable of forgetting -- fearful of what this means, she gets a boyfriend in order to prove herself "normal". She later makes friends with a queer schoolmate, Valentin, and he takes her to some gay bars; in one of these, she happens to meet the blue-haired girl: Emma.
Emma and Clémentine start out as friends, on account of the former's being in a relationship and the latter's still trying to come to terms with her sexuality, but in the long run their attraction to one another can't be denied, and they become lovers. However, they don't automatically get a happily-ever-after: there are still beast that must be conquered, the most dangerous of these being homophobia, both external and, in Clémentine's case (and perhaps in Emma's too?) internal.
The novel doesn't have a "happy ending" in the usual sense -- that much is clear from the first pages on, the bulk of the story being told in retrospect -- but neither does it end with a breakup or Clémentine leaving Emma for a man (I feel like this should be stated clearly). I'm reccing it because I think it's a moving story, and an important one; I also really like the art -- mostly kept in grey, black and white, with occasional use of colour, first and foremost as the leitmotif of blue in Emma's hair.
You can buy the novel for instance
here (in French) or
here (in English); following the movie's success, there have also been various translations to other languages, and your local library might own a copy or two. The creator, Julie Maroh, has a blog
here (mainly in French).