Another approach is to have characters from one universe cross over to the other. Maybe Darth Vader could end up in Gotham. His imposing presence and dark powers would be a huge shock to the criminals there. He could even form an unlikely alliance with Batman, with Vader's goal being to find a way back to his own universe while Batman tries to keep Gotham safe from this new, extremely powerful threat.
One way to merge the two universes in fanfiction could be through a plot device like a dimensional rift. For example, a Sith Lord could accidentally open a rift that leads to Gotham City. This would bring the dark and brooding atmosphere of The Dark Knight into the Star Wars universe. Batman might find himself in a world of lightsabers and the Force, and his detective skills could be put to the test in a whole new way.
In fanfiction, it could also be interesting to explore how the concepts of the Force and the Dark Side compare to the morality in Gotham. The Jedi's code of honor could be contrasted with Batman's no - killing rule. A character like Luke Skywalker could come to Gotham and try to inspire the people there with his Jedi teachings, while also learning from Batman about how to fight crime in a more 'grounded' way.