They would probably be very concerned. They might first check his vital signs to make sure he's okay. If they find nothing physically wrong, they'd start to consider other possibilities like magic or mind - control.
The members of the Justice League would respond in different ways. Superman, being the all - around good guy, would be immediately worried and try to find a solution. He might try to use his heat vision in a gentle way to see if it could rouse Captain Marvel. Batman, on the other hand, would be more suspicious. He'd start looking for any signs of foul play. Wonder Woman would be both concerned and protective, standing guard over Captain Marvel while the others investigated. The League would also likely communicate with each other, sharing their thoughts and theories about why Captain Marvel has fallen asleep.
The Justice League's reaction would depend on the situation at the time. If they were in the middle of a battle, they'd have to quickly adjust their strategy without Captain Marvel's strength. Some might be angry that he's out of commission at such a crucial moment. Others, like Flash, might try to use his speed to keep the enemy at bay while the rest figure out what to do with Captain Marvel. And after the initial shock, they'd definitely start looking for a way to wake him up.
In such a fanfic, perhaps the other members of the Justice League might start to worry about Captain Marvel. They could think it's some sort of strange attack or the result of a new, unknown power affecting him. They might gather around him, trying to figure out what's wrong while also keeping an eye out for any potential threats.
In a fanfic, Captain America could fit into the Justice League by being the voice of the common man. The Justice League often deals with big, cosmic threats, but Captain America would remind them of the importance of protecting the ordinary people on the ground. His experience in World War II gives him a unique perspective on the cost of war and the value of peace, which could influence the Justice League's decisions when it comes to using force and resolving conflicts.
Ruby would be shocked and excited by the plot twists. Weiss might be initially skeptical but then intrigued. Blake would try to understand the deeper meaning behind the twists, and Yang would be all for the unexpected turns that led to more action.
The Flash might initially be in denial. He's used to Batman always having a plan and his death would be a huge shock. He would then turn his speed into a tool for investigation, trying to find out exactly what happened. Green Lantern could feel a sense of loss but also be spurred into action, using his ring to try and prevent future tragedies like Batman's death. He might create constructs in Batman's memory to inspire the team.
The Justice League as a whole would have a diverse range of reactions. Some members like the Flash would be all for it, seeing it as a fun exploration of Batman. Others like Wonder Woman might use it as a way to understand how the public perceives Batman's role in the League. And then there are those like Aquaman who might just shrug it off unless it directly affects his interests. The fanfiction could also potentially create some internal discussions within the League about how they are all portrayed in the public's imagination.
Some of them might laugh. They would see the creative and sometimes out - there ideas that fans come up with in the fanfiction. For example, if there's a fanfic where Oliver Queen teams up with a really strange character from the Arrowverse, it could be quite humorous to them.
Some of them might be amused. They could find the different takes on their characters and stories quite entertaining. For example, Superman might chuckle at a fanfic that has him in a comical situation.
He'd fit in terms of values. Steve stands for truth, justice, and the American way, which is not too far from what the Justice League represents. His physical abilities, while not as super as some of the League members, are still impressive and his combat skills would be useful.
They'd likely be intrigued. Batman would study it for plot devices and character development. He might use some of the ideas in his own crime - fighting strategies. Superman would probably be entertained, seeing it as a new form of storytelling about a hero. Wonder Woman might view it as a cultural phenomenon and think about how it reflects on modern society's view of heroes.
Batman would probably be more critical. He'd analyze how the fanfiction portrays his detective skills and his relationship with the other members of the Justice League. He might not like it if the stories make him seem too soft or too brutal, as he has a very specific self - image.