The premise of the film appears to be "fantasy" only in the sense that it is not strictly realistic. However, if we define "fantasy" this way, almost everything can be considered on topic here.
The Simpsons are yellow and have 4 digits per hand. The baby is still a baby after 26 years of the show. The city of Springfield is said to border on Ohio, Nevada, Maine, and Kentucky (Ohio and Kentucky actually do share a border, but Nevada and Maine are hundreds of miles away from either). Homer has caused several nuclear meltdowns, but is still the safety inspector of a nuclear power plant. This is not realistic.
The old TV show Murder She Wrote was set in a small New England town, but someone was murdered there every week1. The local police force was incapable of solving the crimes, and instead of hiring more detectives, they asked a local mystery writer to do their jobs for them - every week. The townspeople didn't have a problem with the incompetence of their police force, nor did they complain about having the highest per capita murder rate in the country. This is not realistic.
However, neither of these shows can be considered as true "fantasy". Wikipedia defines the fantasy genre as follows:
Fantasy is a genre of fiction that commonly uses magic and other supernatural phenomena as a primary plot element, theme, or setting. Many works within the genre take place in imaginary worlds where magic and magical creatures are common.
The Oxford Dictionary largely agrees with this description:
A genre of imaginative fiction involving magic and adventure, especially in a setting other than the real world.
This definition would appear to suggest that neither The Simpsons, nor Murder She Wrote, nor Inside Out fit the criteria for fantasy.
It seems even less likely that Inside Out could be considered "science fiction". Again, Wikipedia defines the science fiction genre as follows:
Science fiction is a genre of fiction dealing with imaginative content such as futuristic settings, futuristic science and technology, space travel, time travel, faster than light travel, parallel universes and extraterrestrial life. It usually eschews the supernatural, and unlike the related genre of fantasy, its imaginary elements are largely plausible within the scientifically established context of the story.
And again, the Oxford Dictionary largely agrees:
Fiction based on imagined future scientific or technological advances and major social or environmental changes, frequently portraying space or time travel and life on other planets.
Although Inside Out appears to include a fantastic conceit - i.e., the portrayal of emotions as actual, personified entities - it doesn't seem to fit either of the categories relevant to this site.
As the question has already been answered by several people, and those answers have attracted upvotes, it would be unfair to delete it out of spite, and thereby deprive users of well-earned reputation increases. The best option is clearly to migrate the questions to the Movies and Television SE site.
1 The show is set in the fictional town of Cabot Cove, which was based on Kennebunkport, Maine. Kennebunkport has a population of 3,500 people. The series lasted for 12 years, at 13 episodes per season, which would have killed off about 160 people, or nearly 5% of the population.