Sure, Rachel Dawes is part of the Batman comic world. Her presence adds depth and complexity to the overall narrative of Batman's adventures in Gotham.
One possible scenario in Batman saves Batgirl fanfiction could be that Batgirl is in a dangerous situation, like being held captive by a powerful villain. Batman, with his detective skills and combat abilities, manages to find her location and battles the villain to rescue her. It's a classic superhero - damsel in distress (although Batgirl is also a superhero in her own right) situation that often plays out in fanfiction.
One common theme is the exploration of their relationship in different universes. For example, in some fanfics, they might be in a world where Gotham is more peaceful, and they can focus more on their personal relationship without the constant threat of villains.
You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). It has a large collection of fan - created works, and you're likely to find several 'Batman and Rachel' fanfictions there. Just use the search function and type in 'Batman and Rachel' and you'll get a list of relevant stories.
There might be a fanfiction where Batman has to save Rachel from a new super - villain in Gotham. This could explore their relationship deeper as Batman realizes how much Rachel means to him while fighting to keep her safe. Maybe in this story, Rachel also plays a key role in helping Batman understand the villain's motives better.