Begin by making the ginger simple syrup. Peel and grate the ginger. Add it together with the sugar and cold water to a saucepan. Bring it to the boil and stir until the sugar dissolves. Cover and let steep for 15 minutes. Strain, discard ginger pieces and set simple syrup aside.
In a blender add frozen peaches and ginger simple syrup. Blend until completely pureed then place into the refrigerator to cool.
Add ice cubes to a cocktail shaker and fill half way with peach puree. Top off with Champagne and shake vigorously to combine. Pour into Champagne glasses and repeat process as needed.