Add gin, fresh lemon juice, and simple syrup to a cocktail shaker filled with ice.
Shake vigorously for 10–12 seconds until well chilled.
Double-strain into a chilled Champagne flute.
Top with Champagne, pouring slowly down the side of the glass to preserve the bubbles.
Stir once gently with a bar spoon and serve immediately.
The French 75 is named after the French 75mm field gun used in World War I - the drink was said to have a kick just as powerful. For a richer, more spirit-forward variation, cognac can be substituted for gin, which is actually closer to some of the earliest recorded recipes.
My Bar Shelf reads your shelf and shows you every cocktail you can make from what you already own, including French 75.