A story could be set around the idea that there is a hidden society of Parselmouths who have their own code and magic. Harry gets drawn into this society and has to learn their ways and secrets. He might find that Parseltongue is not just about talking to snakes but can be used in more complex and unexpected forms of magic, like unlocking hidden chambers in Hogwarts that are only accessible through Parselmouth incantations.
The Parselmouth could start to understand the emotions and thoughts of snakes more deeply. For example, they could sense when a snake is about to attack or when it's feeling threatened, not just what it says.
It could be a symbol of Gryffindor's spirit in the fanfic. When Harry wields the flame, he is representing all the brave and noble qualities of the Gryffindor house, and it might inspire others around him to be braver too. Also, the flame might have some special abilities like being able to break dark spells or protect the innocent.
Maybe he stumbles upon it during a time of great danger in the fanfic. For example, when facing a powerful dark wizard, he might feel an unusual warmth and strength within him, and then realizes it's the power of the Gryffindor flame.
It could be a key to unlocking hidden secrets within the Gryffindor house. For example, there might be a secret chamber that only the one who can control the flame can access, and inside there are powerful spells or artifacts.
Maybe it's to fit certain moral or ethical standards set by the fanfiction community. For example, some interpretations of Harry's character might be considered too dark or out of character, so they censor it to keep the overall tone positive and in line with the general perception of Gryffindor values.
In some fanfictions, the sword is portrayed as having a sentient nature. It can communicate with the wielder, guiding them through difficult situations. For instance, it might give advice on how to defeat a powerful dark wizard.
The sword in fanfiction can also be a symbol of hope and courage in different ways than in the original books. Maybe it has the ability to glow brighter in the presence of true Gryffindors from other magical schools, uniting them in a time of great danger.
It could have completely changed the dynamics of the story. Draco's character might have developed differently surrounded by Gryffindor's values and friends.