Congress included in copyright law a statute that creates very specific exceptions to the rights of copyright owners. The public performance of a motion picture -- even if no admission fee is charged -- to attract people to a non-profit's group meeting is NOT one of the exceptions.
But because your group is non-profit [and presumably socially beneficial] and because you're not charging an admission fee, you should ask the owner of the copyright in the movie for a one time license to publicly perform the movie. A simple search via Google should be all that it takes to track down the name of the production company that created the movie. Good luck.
The film's copyright owner has the exclusive right to exhibit and perform their film in public (as well as the right to make copies of it, alter it with derivative works, distribute it, etc.). Their rental to you only allows home/personal use, not public/commerical use, whether for a charged admission or not, since your group would get a benefit out of drawing people to your meetings.
You can certainly try asking the film's owner for permission to screen their film at one of your non-profit group's meetings, but unless your group has a fairly high profile and a persistent business affairs staff, I think it's unlikely that you'd get a response.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Both Daniel and Pamela are perfectly accurate: it is not legal for you to show that movie in public without the express permission of the copyright holder as the rental license doesn't cover it. Daniel made a great point about possibly securing a gratis license from the copyright owner to show their work to the public. Depending on your charitable purpose this may be possible, but as he mentioned, it will be up the copyright owner to grant that license. Also, this is a great time to point out that any unauthorized usage of copyright is still considered infringement even if there is no monetary exchange - e.g. just because you don't charge does not mean that the use of the copyright without permission is allowed.
Reach out to the producers (if they are the copyright holders) and ask permission.
**DISCLAIMER**The information contained in this answer post should not be construed, considered or relied upon as legal advice. You should contact and engage a qualified licensed attorney in your jurisdiction as each state's laws are different. No attorney-client relationship is established by way of answering your question.