In a medium saucepan, combine the sugar and water. Bring to a boil, stirring until sugar is dissolved, about 5 minutes. Remove from heat and let cool for 30 minutes. Mixture yields just a little over 2 cups.
Place raspberries in blender with 1 1/4 cup simple syrup, pinch of salt and 1 Tbsp. lemon juice. Puree until smooth. Strain raspberry mixture through a fine-mesh sieve set over a large measuring cup, pressing on solids to release puree. Set aside.
Rinse blender. Place the peaches in blender with the remaining simple syrup, a pinch of salt and 2 Tbsp. lemon juice. Puree until smooth.
Place about 1/4 cup raspberry mixture into the bottom of each 9 oz. cup and freeze until partially frozen, about 30-45 minutes. Next, add about 1/4 cup peach mixture to each cup. Return to freezer for 30-45 minutes, then insert stick and add final layer of raspberry mixture, about 1/4 cup in each. Return to freezer for 30 minutes. After 30 minutes, add one fresh raspberry to top of popsicle (as pictured) and continue to freeze until solid, about 5 hours.