In a small bowl, dissolve the yeast and sugar in warm water. Let it sit for 5 minutes until it becomes frothy.
In a large mixing bowl, combine the flour and salt. Make a well in the center and pour in the yeast mixture and olive oil.
Mix the ingredients together until they form a cohesive dough.
Transfer the dough to a lightly floured surface and knead for about 5 minutes until it becomes smooth and elastic.
Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm place for 1 hour until it doubles in size.
Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper.
Punch down the risen dough and transfer it to the prepared baking sheet. Shape it into a rough rectangle.
Using a sharp knife or a baker's lame, make slashes across the dough to create a leaf-like pattern.
Cover the dough with a clean towel and let it rise for another 30 minutes.
Bake the fougasse in the preheated oven for 20-25 minutes until golden brown and crispy.
Remove from the oven and let it cool on a wire rack before serving.