One interesting fan fiction could be about them meeting again years after their breakup in a small coffee shop. Taylor is there writing a new song and Jake walks in by chance. They exchange glances and start a conversation that rekindles old feelings.
You can try some fan - fiction websites like Archive of Our Own (AO3). There are a lot of user - generated stories on there, and you might find some great Taylor Swift and Jake Gyllenhaal fan fictions.
She could also have been inspired by classic love stories. Romeo and Juliet is an obvious influence, as the song has many parallels to that story. The idea of two young people in love against all odds might have been what sparked her creativity.
Basically, 'Love Story' is about a romance that seems impossible at first but eventually finds a way. It's filled with Taylor Swift's heartfelt emotions and beautiful imagery.