Combine champagne, 1 cup sugar, and 1 1/2 cup water in a small saucepan and heat over medium high heat. Stir to dissolve the sugar. Once bubbling, reduce to a simmer and cook for 2 minutes.
Remove from the heat and pour into a high powered blender.
Add the strawberries and salt and blend on high until fully pureed and smooth.
Pour mixture though a fine mesh strainer and back into the small saucepan.
Meanwhile, cook the balsamic and 1/4 cup sugar over medium heat for about 8 minutes until it has reduced slightly and become syrupy.
If serving hot, serve the soup right away garnished with fresh basil, drizzled with 1 tablespoon of the balsamic reduction, and sliced strawberries. If serving cold, chill for 1 hour and then serve garnished the same way.