In a bowl, combine all the ingredients. Season with salt and pepper. Set aside.
Preheat the grill, setting the burners to high. Oil the grate.
On a floured work surface, divide the dough in half. Roll one piece of dough at a time to a circle about 11 inches (28 cm) in diameter.
With a knife or kitchen shears, make six incisions on each piece of the rolled-out dough, stopping about 1 inch (2.5 cm) from the edge. Brush with the aromatic oil and sprinkle with fleur de sel.
Reduce the heat to medium-low. Lightly pull the dough apart to open the incisions then place them oiled-side-up on the grate.
Close the lid and cook for 4 to 6 minutes or until the bottom is golden brown. Flip the fougasse and brush with seasoned oil. Sprinkle with fleur de sel. Continue cooking for 4 to 6 minutes, or until the dough is thoroughly cooked. If needed, move the fougasse around on the grill to cook more uniformly. Flip the fougasse onto a board and brush with the remaining seasoned oil.