Place the applesauce, apricots, and sugar into a non-reactive 2-quart heavy-bottomed saucepan over medium-high heat. Mix together, then add the raspberries. The raspberries will dominate the flavor. If you want apricot-flavored Pate de Fruit, omit the raspberries. Using a hand-held immersion blender or whisk, combine all of the ingredients until smooth and homogenous. As the mixture cooks, the natural pectin in the fruit will cause the mixture to thicken. Continue to cook until it is thick, mixing constantly. To test for the correct consistency, dip a whisk in the mixture and hold horizontally in front of you. Watch as the mixture drips off the whisk and back into the pan. If the mixture stays on the whisk and beads up into small balls, like pearls, it is ready. If it drips back into the pan in thin strands, it needs to be cooked a little longer.
When the mixture is a bit thicker than jam, pour it into a spouted container. Fill either a half-dome or triangle shaped flexipan, depending on the desired design of the jewels and let rest for 4 hours at room temperature. When the mixture has set, remove and roll each jewel in sugar. If you do not have a flexipan, you can pour the Pate de Fruit into a 10-inch bottomless tart mold or cake ring placed on a parchment paper-covered baking sheet. Let the Pate de Fruit cool and set, about 3 hours at room temperature. When the mixture has set, remove and roll each jewel in sugar. To unmold, run a sharp paring knife between the fruit and the mold and lift off the mold. (At this point the Pate de Fruit can be stored, well wrapped in plastic and in an airtight container, for up to 2 months.) Sprinkle the top of the Pate de Fruit with a thin layer of sugar and flip it onto another sheet of parchment paper. Remove the parchment that is now on top. Sprinkle this side with more sugar. Using a wet chef's knife or cutter, cut the Pate de Fruit into any shapes. Roll each piece completely in sugar and serve. Do not store in the refrigerator, as the humidity will make the sugar melt.