Preheat the oven to 375ºF (190ºC). Line a baking sheet with parchment paper.
On a lightly floured surface, roll the dough to a 14-inch (35cm) circle, turning it over and dusting lightly with flour, to keep it from sticking to the counter.
Brush off any excess flour and transfer the dough to the prepared baking sheet. (At this point, you may want to chill the dough for a few minutes, as the frangipane may be a bit tricky to spread if the dough feels warm.)
Smear the frangipane on the tart dough, leaving a 2-inch (5cm) rim around the edges. (If the frangipane is quite thick, you can dollop it in 5-6 places over the tart dough, which'll make it easier to spread.) Place the apricots on the frangipane and put cherries in the spaces between the apricots. Fold the edges of the dough over the fruit to make a crust. After pleating and folding the rim, make sure there are no "gullies" in the pleats for fruit juices to run out of. Pinch together any cracks.
Brush the rim of the crust generously with melted butter then brush the remaining butter over the fruit. Sprinkle the rim with about 1 tablespoon of coarse or granulated sugar. Then sprinkle another 1 tablespoon over the fruit. (If using fruits like nectarines and peaches, you can reduce the sugar to a few teaspoons.)
Bake the tart until the crust is well-browned and the fruit is cooked through, about 40-50 minutes. Remove from the oven and let the tart cool for 5 to 10 minutes, then brush the fruit with apricot jam.