First, start with their existing personalities. Yumi is often serious and focused, while William can be a bit brash. Have them interact in situations that force them to understand each other better. For example, in a group mission on Lyoko, they might have different ideas on how to approach a problem. By working through these differences, their relationship can start to grow.
I'm not sure who exactly Ms Nelson is without more context. She could be a teacher, a storyteller in a community, or just an ordinary person known for her storytelling skills.
Given the title, Ms Shields is the key figure in 'A Christmas Story'. She could be an elderly woman with a lot of wisdom about Christmas traditions. Or she could be a young woman facing some challenges during Christmas time. Maybe she has a special gift or talent that is related to Christmas, like being an amazing baker who makes Christmas cookies for the whole neighborhood, but there's more to her story that unfolds during the events of the narrative.
One idea could be a story where William, after being rescued from XANA's control, has trouble fitting back into normal life at Kadic. Yumi could be the one to help him through it, and during this process, they discover new feelings for each other. Maybe they have to face some remnants of XANA's influence together, which makes their bond stronger.
Growth and self - discovery are other themes. The relationship between the two can be a catalyst for each character to learn more about themselves, as they interact and face different situations together in the fanfic stories.
One great place to start looking for Sachiko x Yumi fanfic is on fanfiction.net. There are often many different takes on their relationship in the fanfics there.