To make the ginger syrup, peel and slice the ginger root into thin pieces. In a small saucepan, combine the sugar, water, and sliced ginger. Bring the mixture to a simmer over medium heat, stirring occasionally until the sugar is completely dissolved. Once dissolved, remove the syrup from the heat and let it cool completely. Once cooled, strain out the ginger pieces and set the syrup aside.

Wash the peaches and lemons thoroughly. Slice the peaches into thin wedges and cut the lemons into slices as well. Add the sliced peaches and lemons to a 2-quart pitcher.

Pour the bottle of white wine, peach schnapps or peach liqueur, and ginger beer into the pitcher with the sliced fruits. Give it a gentle stir to combine all the ingredients together.

If you prefer a sweeter sangria, you can add some of the prepared ginger syrup to the pitcher. Start with a small amount and taste, then add more if desired. Stir well to ensure the syrup is evenly distributed and dissolved.

Cover the pitcher and place it in the refrigerator to chill for at least 2-4 hours before serving. This allows the flavors to meld together and the sangria to become nicely chilled. When ready to serve, pour the ginger beer sangria into glasses filled with ice, garnish each glass with an orange slice if desired, and enjoy your refreshing and flavorful drink!