Coarsely chop the peaches in a food processor. Measure out 3 cups.
Place the white grape (or apple) juice, lemon zest, and lemon juice in a large saucepan. Gradually stir in the pectin; continue stirring until completely dissolved. Place over medium-high heat and bring to a full rolling boil, stirring frequently. Boil hard for 1 minute. Remove from the heat. Immediately stir in the chopped peaches. Stir vigorously for 1 minute. Stir in the sugar to taste until dissolved.
Divide the jam among six 8-ounce canning jars, leaving at least 1/2 inch of space between the top of the jam and the top of the jar (this space allows the jam to expand as it freezes). Cover with lids, and let the jam stand at room temperature until set, about 24 hours. Store in a refrigerator or freezer until ready to use.
