In general, the performance or showing of films for public viewing does not fall under the fair use exception. It does not matter whether the showing is free or whether admission is charged; this is not considered a fair use under U.S. copyright law.
Often in this situation, you will need to seek permission from the copyright owner by acquiring a public performance rights (PPR) license in order to show the work. Generally, there is a charge for a PPR license, one that can range from $100 to $1,000, depending on the work and who owns the copyright. The University Library System cannot acquire PPR licenses for films for you or your group.
However, according to copyright lawyer and specialist, Kevin D. Smith in Owning and Using Scholarship: An IP Handbook for Teachers and Researchers, there may be a fair use defense for student groups showing a video if the showing is done for truly educational purposes. For example, if a student group is "discussing a topic related to the curriculum or in some other way that is clearly educational" (p. 102), it might be possible to use the fair use exception under U.S. copyright law to show a film to the group without acquiring a PPR license.
Such a group would have to be specific and limited and use must be for educational or curricular purposes.
This, like much in copyright law, is an "it depends" situation. Departments should consult with sponsors, governing bodies, or university officials and policies to determine what the university allows.
Often the performance or showing of films for by university-affiliated student groups, clubs, and organizations may not fall under the fair use exception of U.S. copyright law. The intent of such showings is generally for entertainment, not for face-to-face teaching.
The performance of or showing of films for public viewing (whether admission is charged or not) as part of a film series does not fall under the fair use exception.
No matter how educational the setting may be or how tied to the curriculum the showing may be, this is generally considered a showing for entertainment purposes. Even if the showing is conducted by a student organization, such as a film society, this would still not be considered fair use.
Thus, in order to show the films, you will need to seek permission from the copyright owner by acquiring a public performance rights (PPR) license.
According to copyright lawyer and expert, Kevin D. Smith, showing films, videos, and TV programs as part of a training program for professional groups may fall under fair use. (See Owning and Using Scholarship: An IP Handbook for Teachers and Researchers, p. 102.)
Again, this may be an "it depends" situation. The group or entity interested in showing the film, video, or TV program may need to consult with sponsors, governing bodies, or university officials and policies to determine what is allowed.
Adapted from "Copyright and Intellectual Property Toolkit" by University of Pittsburg Library System licensed under Creative Commons Attribution 4.0 International License. 
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