Lightly oil an 8-by-8-inch baking dish. Line the dish with a piece of wax paper that extends 4 inches beyond the rim.
In a food processor, puree the thawed raspberries with the raspberry jam and the 1 cup of sugar. Strain the puree into a medium saucepan. Boil the puree over moderately high heat, stirring often, until reduced to 3 cups, about 10 minutes.
In a small bowl, sprinkle the gelatin over the water in an even layer. Let stand until the gelatin softens, then heat the water in a microwave for 20 seconds, until the gelatin dissolves completely. Stir the melted gelatin into the raspberry puree, then pour the mixture into the prepared dish. Let cool to room temperature, then cover with plastic wrap and refrigerate overnight.
Just before serving, unmold the pâte de fruit onto a work surface. Peel off and discard the wax paper. Using a sharp knife, cut the pâte into 1-inch squares or triangles. Spread about 1/2 cup of sugar in a shallow bowl. Roll the pieces in the sugar to coat. Arrange on a platter and serve.