Perhaps the child is on a quest to bring back a lost magic that was present in the past but will be crucial for the future. Fred and Hermione are initially skeptical but as they see the child's abilities and the evidence of the disappearing magic, they start to believe. Together, they embark on a journey to find ancient spells and artifacts that can restore the magic, all while dealing with the challenges of time travel and the secrets the child holds.
Their relationship would likely become more serious and responsible. They'd have to put aside some of their youthful antics as they now have a child to think about, even if it's from the future. There would be a new level of trust and understanding as they work together to deal with the situation.
It could be that Fred was involved in some sort of prank that backfired and affected Hermione negatively. For example, if he was testing a new product from Weasley's Wizard Wheezes and it made Hermione look foolish in front of others. An irate Hermione would be a force to be reckoned with. Fred, realizing the magnitude of her anger, quickly decides to run. He might be thinking of ways to make it up to her as he runs, like coming up with a grand apology or a way to reverse the damage he's done.
One possible plot could be that the child from the future comes back to prevent a great disaster. Maybe a dark wizard in their future time has found a way to rewrite history and the child has to make sure Harry and Ginny meet and fall in love at the right time. The child might also have some special powers inherited from their parents which they use to face various challenges in the past.
It could also be that they run away for a more personal reason. Maybe Fred has feelings for Hermione that go against the social norms in the wizarding community. They run away to be together and explore their relationship away from the prying eyes and judgmental attitudes of their friends and family.
Well, it could be a story where there's a big misunderstanding. Maybe Hermione thought Fred was about to play a prank on her that would cause harm to someone, and in her haste to stop him, she accidentally kicks him in the balls. Then it might lead to a whole series of events like Hermione feeling extremely guilty and trying to make it up to Fred while Fred is initially angry but then realizes it was a mistake.
It could be a jealous wizard who was once in love with Hermione. Discovering she has a child with Fred, this wizard might seek to harm the child out of spite. He could use dark magic to try and kidnap the child or cause trouble for the family.
One idea could be that the child has unique magical abilities that neither Fred nor Hermione expected. Maybe the child can communicate with magical creatures in a way no one else can. Another plot could be the secrecy around the child's existence causing all sorts of misunderstandings among the Weasley family and Hermione's friends. For example, they might suspect Hermione of being involved in some dark magic when they notice her acting strangely to protect the secret.
Fred could use his knowledge of the Weasley family's magic tricks and inventions. He might have some secret gadget or spell that can break through the barriers or spells that are being used to torture Hermione.
Perhaps their child would be a key figure in bringing about more positive relations between the wizarding world and the Muggle world. Given Hermione's Muggle - born background and Draco's pure - blood status, the child could use their unique position to advocate for better understanding and cooperation. They might even start a new organization at Hogwarts dedicated to this cause, which would be an exciting plot point in the fanfiction.
Maybe it could be a story where Hermione is cold and Fred offers his clothes. Then it becomes a cute moment that leads to a deeper friendship or some unspoken feelings between them.