You need to understand Chat Noir's character well. He is charming but also has insecurities. To write about his worries, you can show his internal monologue. For instance, if he's worried about being overpowered by an akuma, write how he's constantly thinking about strategies while also fearing failure. Use descriptive language to convey his emotions.
To write a 'Chat Noir Worries' fanfic, start with a strong hook related to his worry. Let's say he's worried about losing his Miraculous. Begin the fanfic with a scene where he almost loses it. Then, develop the story by showing how he tries to prevent that from happening. Include other characters like Ladybug, who could either help or add to his worry. Also, make sure to end the fanfic in a satisfying way, either by resolving the worry or leaving it open - ended for the readers to think about.