The film you want to base your game on is probably covered by copyright and likely trademarks. For purposes of the question I'll assume it's not in the public domain (if the film was made before 1926 for example).
If you used the film to create your game, it would be a derivative work. Derivative works require the consent of the copyright owner. Distributing it without their permission would leave you open to lawsuits for copyright infringement, unjust enrichment, and possibly others.
Fair use/fair dealing likely doesn't apply here. This isn't criticism, parody, or a transformative use.
You may be able to get away with this by flying under the radar if you don't distribute it for profit or on any large scale. Some studios are more litigious than others and some accept that leaving fan works alone is better than the bad publicity that comes with shutting them down. However, this is entirely reliant on the goodwill of the studio.
The legal way to do this is to get in touch with the copyright holder and ask permission. This may be in return for something else- usually money, royalties, and/or some creative control over your work. This may not be feasible though as a large company may simply ignore such requests from random people. Note that a lack of a response in this case is not permission.