Sorry, but that is totally insane and contradictory because quite simply it's not technically possible. Either you live with the reduced quality and limitations of an animated GIF or you use a static background. And even then I would predict that your GIF fiel may be way to heavy for web site use. You really need to reconsider your strategy and read up on web design in general. this simply cannot work the way you want it to.
Rick and Mylenium are right; you want to use an H.264 video with some code to loop it in the background. GIF's have huge file sizes and poor quality compared to a properly compressed video stream.