I actually see it more like a mix between Star Trek, Battlestar Galactica, and Star Gate.  I think done right it could have a lot of potential.  It would be hard to be able to reflect the galactic scale that the game can.  Think of the core factions with several random (non-core) other factions mixed in eating Torian Soup, just as some Torian freedom fighters attacking the Great Hall and erupting a massive galactic war!!!

All the possibilities....

I think a normal movie would not work, since a movie needs to follow some characters - but GalCiv is not about individuals, it is about whole civilizations. Of course you could write a story that is located in the GalCiv universe, but it would not be "GalCiv the movie".

If anything a fake documentary would be the way to go. You could do some documentaries about the colonizations, the techs, the wars in the GalCiv universe with fake footage, some historians who explain why the Drengin liked to eat Torians and interviews with important people like Jenna Casey or N-1. Basically like the documentaries about World War 2 or the Cold War Period you see on TV.

Wishing for a movie is a bit much when we don't even have voice acting in game or faction specific cutscenes.

I have in my collection of old sci-fi a book called The Forever War by Joe Haldeman.  As I recall, it gives the perspective of a space war from the viewpoint of the crews on relativistic speed ships living on a time scale greatly independent of that on the individual planets they protect/threaten.  I have always envisioned my games of GalCiv as that kind of plot, with the administrators of the galaxy also caught up in the isolating nature of time warped space travel.  I think you could use that mechanic to tell a people based story that also spanned the lifetime of an empire.  You could use the concept of the relativistic days and weeks in GalCiv turns to cover sprawling empire changes happening in seemingly brief time spans.