If you're thinking of the ones I'm thinking of (the champaign bottles), that's pure apple juice carbonated and bottled. You can duplicate it with a keg setup.
Alternatively, if you want to bottle it, get apple cider w/ no preservatives (preservatives will kill the yeast). Dissolve a small amount of dry brewers yeast in warm water - about 1/4 tps for 2 liters of cider. Fill a two liter soda bottle with the apple cider and add yeast slurry. Condition at room temperature for about 5 days. Chill it and test the carbonation. If it's too flat, adjust your yeast volume for the next batch. Once you perfect it in the soda bottles, then move on the the champaign bottles. With this method, you will get some yeast sediment and a negligible amount of alcohol. Not enough to even notice and definitely not enough to get drunk on.
I'm adapting this recipe from a soda extract recipe, so I'm guestimating the amount of yeast to use. It may take more or less. Good luck and let us know how it comes out.