There are hundred of tools in GNU Linux plus a lot of multimedia Linux distributions that are near of your dreams and that authorize you to edit a movie.
Generic GNU Linux distros like Debian, Ubuntu, OpenSuse, Mandriva, etc, may contain some video and sound tools but you will need surely to add the missing ones and then fight a little bit with the packages and the needed dependencies, if not to compile the whole thing to get what you need and want. These distributions are generalist by default, so you will find in them a lot of tools put there to please at a maximum of people but that you will probably never use.
You can then take a look to the multimedia distributions, but you will face the same problems. They are specialized distributions, this means mean that you will find here too a lot of tools to cover the video, sound and image aspect and surely the one you want for video stuff, but as the generalist distros that will come with a lot of unnecessary tools that will perhaps cause some problems if you delete them because linked to the same dependencies you are using too.
You can use of course these (good) distros "as it", without any problem. Until perhaps a release that will change some dependencies, or if you know how to compile in Linux to get the only tool not in the distro or to update manually the one you want to have for some interesting features. Generally the beginning of some problems in stability if you are not an expert. These multimedia distros are also mixing complex and simple tools. Their goal is to reach the maximum of people, so a professional tool will be given as also a semi-professional one and a very simple one. To give an example for video editor is not rare to find on the same distribution Cinelerra, Kdenlive, OpenShot, Kino and Pitivi!
In fact there is no in Linux a professional distribution for movie makers but only professional movie makers dealing with Linux distros and tools to make their movies. It's very difficult indeed to really imagine what a pro will effectively need. If Charlie Chaplin was of this world again and using a computer he would need everything! Tool to write a scenario, other ones for the music, other ones for post-production things, etc. Not anybody is Charlie Chaplin and for sure will not need all this. After all, a movie is rarely done by a single person, it's a teamwork that implicate different people with different competencies. And which movie type are we talking about? Movie with flesh and bones actors? 3D or 2D or animated puppets ones? Or even, a mix of all these things? In which genre? Action, Documentary, Sci-Fi ? As you can see there as much movies as genre and type that will necessitate finally some specific tools surely not in a distribution. Making then a movie oriented GNU Linux distro for pro movie maker seems challenging.
Making a movie of any genre obey to incontestable five steps : Development, pre-production, production, post-production and diffusion. In every steps tools are used to facilitate the work and the passage to the next step until the end. Determining which exact tool is needed through the thousand existing ones, will be facilitated if we define some criteria. You can refine also the search if you know which public you want to raise.
The tool we plan to make is dedicated to the professional movie maker. This exclude then the occasional one that need some Linux tools to edit his holidays or anniversary videos. For these ones the generic or multimedia GNU Linux distros are very sufficient. It's not ostracism but a clear way where we want to go and the people we want to reach. By professional movie maker we also mean the ones working with flesh and bones actors as the animators working with imaginary 2D, 3D and stop-motion characters.
Concerning the tools:
With all these criteria we will be able then to determine in a first step all necessary tools to see if they fit the needs in every production and then to build a workflow platform that will be named: Apertux. It will be not a simple distribution but a compendium of different tools, approaches, tutorials, encapsulated in a production pipeline, workflow that all "actors" involve in a movie production will need to build it and to communicate each others.
Apertux is link deeply to the apertus° project. apertus° users will be able to work directly with Apertux to edit their movies but also will find in the workflow the necessary tools to manage their apertus° camera. This don't signify that you will need an especially Apertus camera to work with the distro. Apertux will be open to all movie makers or video camera owners. Being an open community we will take attention to made this tool open too.
Welcome then to Apertux and no not hesitate to participate by your contribution and your comments to the building of this new tool as to support the apertus° video camera project.
More details can be found in Apertux wiki page