She's a very good player from Seirin's basketball team.
Before the start of the storyline of GTO, around two years ago, she had an episode where some bullies were picking on her due to her particular height, evolving the situation for the good showing Murai coming in her defence.
A really tall girl introduced as having a crush on Murai, she writes him a love letter and signs it as "F in class 2"; although she should have specificated more, since this F leads Murai and his group to think as an initial of a last name rather than a first name and will bringing the situation towards an unwanted direction (Murai will end up thinking that F is Akane Fujita, a very popular girl in the school, and will ask Kujirakawa to help him declare his love for Akane). In the near end however, Fuyumi saves Kunio from getting drowned in the lagoon knowing that he can't swim. Julia actually let Fuyumi leave as she pinches Kunio's ear to stop beating his teacher and tells him that he loses a game of love. Kunio realizes that the letter sign "F" belongs to Fuyumi as he goes after her. Fuyumi is last seen riding a bus as Kunio chases after it before he slips on the ground.
Manga version only: all the above described situation happens in the manga as well, althought Akane Fujita is the anime version of Aoi Fukada from the manga (so in the manga Murai thinks that Aoi sent him the letter and he is in love with her), and Kujirajawa sets him with Fukada, but is not the one Murai thinks.
Also, Fuyumi is sensitive when people makes fun of her height.