A headstrong ex-con desiring a family, falls for the woman who saves his life, but her drug addiction and past horrors may destroy everything.

Thanks James, but her past horrors is her childhood horrors, and my screenplay does have a twist in ACT III. I want to show my Protagonist trying to help his lady through her problems, although she's avoiding talking about her childhood. I'm trying to get away from the typical black themed movies with violence, and gangbanging, and all that other stuff. My Protagonist pursues her and wins her over towards the end of ACT I. He think's she's perfect, but we know she's not. He will start to see something aint' right with her beginning ACT II. I want to show my character trying to move mountains for this lady... but everyone has a boiling point.
I'm still working on my logline, but I do think I've touched on the basics that make up a logline. It took me a few times to understand that... but hopefully I got it... Thanks to Karel

I like the idea. The inciting incident is clear enough, she saves his life. Then as the first act comes to an end and rolls into the second, he begins to fall for her. I just think that the second act needs some work.

Although her drug addiction and past horrors seems interesting it feels a little vague. There's no real action there. I'd rather it say something like 'her drug addiction brings an ex boyfriend felon back into her life..." or something like that. (obviously this isn't your story, just an example) My point is just that this will imply action and a more aggressive protagonist who has a physical goal to overcome, rather than him trying to deal with her emotional baggage.

Hope that helps