This served 20 adults for 3 or 4 hours.
The night before, make an ice ring:
Put a pound of frozen peaches (or your own peeled, pitted, and wedged peaches) into the bottom of a Bundt pan (or any other decorative pan or tupperware). Cover peaches with Sierra Mist Natural (I recommend this only because it is made with sugar not HFCS. You could use 7-Up.). Place in freezer overnight or until frozen solid. To remove, put pan in sink of tepid water to loosen and then put it in the punch bowl trying not to splash (or put it in before the liquids).
4 bottles of chilled, cheap Champagne or Sparkling Wine (I used 2 cheap, 2 moderate bottles because that is what I had on-hand: 2 J Roget, 1 Korbel, and one Frexinet), any brand, any Brut, semi-dry, spumante, etc.
1 bottle of peach schnapps (the cheaper the better...mine was $9.99, but I am pretty sure a cheap-o bottle can be had for $7 or $8).
4 twelve-ounce cans of Peach Nectar (at my grocery store, it was found on the Latino Foods aisle). All the brands said 100% nectar on the front and had sugar/high fructose corn syrup listed as an ingredient. I don't know whether it was sugar or HFCS, but how is that 100% nectar?
1-2 cups of Sierra Mist Natural, to taste
One ice ring with frozen peaches
serve with ladle from (borrowed) punch bowl (or heck, a stock pot would work) into Solo Cups (or you know, champagne flutes if you're feeling fancy)
This recipe would be very easy to scale down to one bottle of champagne (and in fact, I made a three-bottle batch and then a one-bottle batch after it was clear that the punch was moving).