Scrape seeds from vanilla bean with a knife into a small bowl, discarding pod, and stir in sugar and cinnamon.
On a lightly floured surface roll out pastry 1/8 inch thick and cut out two 6- by 5 1/2-inch rectangles. Arrange pastry on a baking sheet and fold edges in on all sides to form 1/2-inch borders, leaving corners unfolded. Form points at corners by twisting ends and pressing them gently onto baking sheet. On pastry arrange plum and apricot slices, overlapping them slightly, in rows and sprinkle with sugar mixture.
Bake tarts in middle of oven until pastry is golden brown, 20 to 25 minutes. Cool tarts on a rack and brush with jam.