King Arthur is indeed a fictitious character, as pointed out by Kirnan Shipka's character.
While the film takes place over Thanksgiving weekend, a shot of Ben's text on Palmer's phone shows the date of Friday, August 5th.
While the film is supposed to take place around Thanksgiving, which always occurs in late November in the United States, the trees are full of green leaves. If it was late autumn the trees would either be bare or have some colored leaves.