"Our love story" or "our happy story" are both ways to describe a couple's romantic journey in Engpsh. You could also say "the story of how we met" or "the tale of our relationship." If you want to be more specific, you could say "the story of how we fell in love" or "the story of how we got married." Ultimately, the way you describe your love story will depend on your personal style and the specific events and experiences that make up your relationship.