Am I allowed to show the interface of a GNU GPL licensed piece of software being used in a TV movie? I'm not in the US, so "fair use" and similar applications do not apply unfortunately.
I think your problem is largely equivalent to the licensing of screenshots, and that problem has a definitive answer: A screenshot of the user interface of some software is a derivative work of that software, and is therefore restricted by the license of that software.
The GPL does not seem to consider screenshots, but it mentions program output:
The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law.
– GPL v3
I strongly assume that a graphical user interface “constitutes a covered work”. However, data displayed with the help of this program is not covered. For example, let's consider a spreadsheet calculator. The user interface with menu bars and widgets would probably be covered by the copyright. However, a screenshot that is cropped to only display data in the spreadsheet would be OK: you provided that data, so you have the copyright.
The Free Software Foundation (which wrote the GPL) interprets this very differently. According to their FAQ, screenshots and videos are free – but that's not actually part of the license.
The output of a program is not, in general, covered by the copyright on the code of the program. So the license of the code of the program does not apply to the output, whether you pipe it into a file, make a screenshot, screencast, or video.
The exception would be when the program displays a full screen of text and/or art that comes from the program. Then the copyright on that text and/or art covers the output. Programs that output audio, such as video games, would also fit into this exception. […]
Keep in mind that some programs, particularly video games, can have artwork/audio that is licensed separately from the underlying GPLed game. In such cases, the license on the artwork/audio would dictate the terms under which video/streaming may occur.
Note that e.g. Wikipedia meticulously tracks the license of all screenshots. For screenshots of non-free programs Wikipedia uses fair-use exceptions in U.S. law, for free programs it keeps the license of the program for the screenshots. The Wikipedia therefore seems to not share the FSF's interpretation of the GPL in this matter. See Wikipedia:Software_screenshots and Commons:Screenshots.
While German copyright law does not have a concept of fair use, it does allow for copyrighted content to appear under certain conditions. The most important exception is citation law (see §51 UrhG). That would be a viable route if your TV movie can be classified as journalism or art, but probably not if it's a commercial entertainment production.