You can't go by the calorie count. The calories in Champagne come from the alcohol, which is completely different than carbohydrates, proteins, or fats. Alcohol is the fourth type of substance your body is capable of metabolizing into energy. That's why many low carb diets warn you to avoid alcohol for the first two weeks - so that your body doesn't try to burn the alcohol instead of learning to burn primarily fats.
Since the process of fermentation is all about the yeast turning the sugars in grapes into alcohol, you don't have many natural sugars in the wine, either. However, Champagne is special because it goes through a secondary fermentation - the one that gives it its signature bubbles. Wineries also add a "dosage" to the Champagne at the end, to add flavor to it. This means that there is actually sugar in a finished bottle of Champagne, where a normal wine has little to none.
The actual carb amount varies wildly from maker to maker, and from year to year, depending on the grapes used, the yeast used, the dosage used, and more. Wineries don't check for carb counts so really it's best just to go with a basic idea that a non-sweet Champagne has around 5g per glass and a very sweet sparkling wine has around 10g per glass. To try to narrow it down more than that is pretty impossible.
Here is a list of common types of Champagne and sparkling wines you will find, ordered from very dry (non-sweet) to very sweet:
Asti Spumanti (Italian)
So if you are aiming for the lowest amount of carbs in your sparkling wine, you want to look for the extra brut styles. You would want to avoid Prosecco and Asti Spumanti, both which are very sweet.
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