Pour gin, simple syrup, and lemon juice into a champagne flute.
Fill the glass almost to the top with champagne.
Use a paring knife to slice a thin layer of lemon peel from the fruit and then roll into a curl.
Rub the outside of the lemon peel around the rim of the glass before placing it in the cocktail. Serve immediately.
Notes
If you want to make those really thin curls that look like the garnish at your favorite bar, this fruit carver is your tool. But for at home, no-frills cocktail making a paring knife will work just fine.