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A true "champagne cocktail"? Sure. Sugar, Angostura bitters, Champagne, brandy, and a maraschino cherry. I am probably not too tight about proportions. I would probably use simple syrup rather than sugar.
If you mean a cocktail made with champagne, I like a French 75. Champagne, gin, lemon juice, simple syrup, as I recall. How do I make it? Whatever the usual recipe is on the internet.
On the subject of cocktails with champagne, one must mention the Kir Royale. Champagne and a bit of crème de cassis (I like just a very little). While something of an '80s/early '90s cliché, it's actually a very nice aperitif when not too heavy on the crème de cassis.