Shooting with real video camera, you’ll notice that noises in the video are not static. they move every frame, which is not the case when rendering video with Cycles. All you need to do is change the ‘Seed’ value for every frame to get different noise pattern. You can manually keyframe ‘Seed’ value, or automate it with curve ‘Generator’.
1. press i over the ‘Seed’ in the first frame to create the first key frame
2. in Graph Editor press n to bring up right side panel. While ‘Seed’ curve is selected, add ‘Generator’ modifier
That’s it. A linear graph is generated, and the seed value will increase every frame.