Preheat the oven to 400 degrees F. Line 2 sheet pans with parchment paper.
Unfold the sheets of puff pastry and cut each sheet into quarters. Place the pastry pieces on the prepared sheet pans and refrigerate while you prepare the apples.
Peel the apples and cut them in half through the stems. Remove the stems and cores with a sharp knife and a melon baler. Slice the apples crosswise in 1/4-inch-thick slices. Place overlapping slices of apples diagonally across each piece of pastry and place a slice of apple on each side. Sprinkle the full 3/4 cup of sugar over all the pastry pieces and dot with the butter.
Bake for 40 minutes, until the pastry is browned and the edges of the apples start to brown. Rotate the pan once during cooking. If the pastry puffs up in one area, cut a little slit with a knife to let the air out. Don't worry! The apple juices will burn in the pan but the galettes will be fine! When the galettes are done, heat the apricot jelly together with the Calvados and brush the apples and pastry completely with the jelly mixture. Loosen the galettes with a metal spatula so they don't stick to the paper. Allow to cool and serve warm or at room temperature.