Total time: 35 minutes
Note: If the tart puffs up in spots while cooking, puncture bubbles with a knife.
In a sauté pan, warm oil over medium heat. Add onion, dried thyme, salt, and pepper; cook until onion caramelizes, 10 to 15 minutes.
Preheat oven to 400° (or temperature on puff pastry package directions). Unfold pastry sheet on a lightly floured work surface and roll out into a 9" x 13" rectangle, about inch thick. Cut in half lengthwise into 2 long, skinny rectangles and transfer to a rimmed baking sheet. Using a fork, prick each rectangle all over. Pinch and fold over 1/2 inch of pastry along all edges of each rectangle to create a border.
Arrange onions on tart shells, then cover evenly with figs and grapes. Sprinkle with bacon. Bake until tarts are puffed and golden brown, about 20 minutes. Remove from oven, garnish with a few fresh thyme leaves, cut each tart into 4 pieces, and serve.