No, I haven't played through FFVII. I don't think that should matter. I've never had to play a videogame to understand a movie before.
Either way, I watched it with two people who had played through FFVII multiple times, and neither of them could tell me why anything was happening. They filled me in on the character names and names of the areas they were in, but it was still just a mismash of people/places/and events that at best were loosely correlated if you played the game, and at worst completely incomprehensible if you hadn't. My friends sort of knew what was going on, but they both admitted it still didn't make much sense, and the sense it did make was pretty bland and uninteresting.
I expect movies to tell a story, call me crazy. AC gave me the distinct impression that it was simply a flimsy pretext to show some cool animation. That's not the direction I want to see videogame movies go in. If I wasn't a fan of both videogames and movies, AC would have turned me off of any future videogame movie.