(Warning: minor spoilers ahead)
Well, in a sense. Much of the background is taken from Harry Potter, and Fantastic Beasts isn't so very different in spirit from some of the later, darker Potter films. Many of the same people are involved - J. K. Rowling having written the script, David Yates returning as director, and David Heyman and Steve Kloves both serving as directors. But the characters are all new; the aesthetic has moved from a remote Scottish castle to 1920s New York; and in general, the film is very different for being an original story rather than merely the adaptation of a book.
I'll start with the good. The special effects are copious and impressive - apart from the numerous spells and explosions, Newt Scamander boasts a remarkable menagerie of magical creatures, our introduction to which is perhaps my favourite scene of the movie. The first half of the film strikes the balance between plot and light entertainment very well.
What of the problems? Ultimately, I think the film tries to do far too much. The second half of the film switches between dark drama and explosions with no rest in-between, which both makes the film less enjoyable and makes the romantic subplots less convincing. I don't object to characters falling in love, but such romances should involve actual conversations between the characters in which they get to know each other. Perhaps Newt and Tina aren't so bad on this front, but the relationship between muggle wannabe-baker Jacob Kowalski and legilimens Queenie is appalling - they begin eyeing each other up as soon as they meet, pay each other a few compliments from time to time, and then by the end of the film Queenie is declaring that she will "never meet another man like you". Perhaps being a mind-reader allows you to get to know people well in short spaces of time, but then the film could have done more to show this.
The 1920s aesthetic works well for set design. The music, however, ruins this impression. James Newton Howard's score is uninspiring, which would be OK, but also for 80% of the film utterly undistinguishable from any other film score. When the characters enter a speakeasy, and in a couple of other places, the music turns into some classic jazz, and these are the finest moments in the soundtrack; they ought to have been the rule, rather than the exception.
The final twist, a reveal in the spirit of Scooby-Doo villains, seemed unnecessary and raised more questions than it answered. Why did Grindelwald, an immensely powerful wizard capable of defeating a score of trained aurors at once, based in eastern Europe, and dedicated to taking over the world, decide to infiltrate the American magical government? How long must he have spent doing this, given that he had achieved a very senior role in this government? And why, once he was captured, was he not immediately killed? It's not like they couldn't have done so, given that several people had already been summarily executed for far lesser crimes. Instead Grindelwald proclaims that "You'll never be able to hold me!" and the American magical president, who had only two minutes earlier ordered one of these executions, mumbles back that "Well we'll do our best."
One also wonders about the differences in social morés between the magical communities of 1920s Britain and the US. The US magicians have apparently overcome both racial and sexual prejudice, to the extent that their president is a black woman. However, they retain a strict legal prohibition upon wizard-muggle relationships. (Curiously this is not matched with any sense of disgust at such relationships). Britain is sufficiently ahead on this count that Newt is able to rather bitingly refer to the American's "backwards view of relationships between magical people and muggles"; has there really not been sufficient interaction between the societies for Britain's liberalism on this subject to rub off on the other side of the Atlantic? (And indeed, where do Canadian witches and wizards stand on this? The main North American school of magic, Ilvermorny, is known to be on the upper east coast, but it is unclear on which side of the US-Canada border it lies; in either case, it seems to be the case that Ilvermorny is the most popular school of magic for both Americans and Canadians. This implies substantial interaction between the two, at a time when Canada was still merely a dominion of the British Empire).
Overall I enjoyed the film, and it was worth seeing (at least at Hungarian cinema prices, which are less than half of UK prices). But I cannot give it more than three stars out of five, and must state my opinion that while this does not plumb the depths of The Cursed Child (which I have declared to be non-canon, but rather an unusually prominent fanfic) one could miss this film, and one would not be any less of a Harry Potter fanatic for it.