Rinse foie gras, pat dry, and discard any tough membrane. Cut foie gras crosswise into 1/2-inch-thick slices. Cover and chill.
Trim off stems and bottom ends of persimmons. Cut each crosswise into 3 equal pieces. Lay a slice on each plate with a cluster of watercress sprigs.
In a 10- to 12-inch frying pan, mix demi-glace, madeira, vinegar, and cream. Boil over high heat, stirring often, until 2/3 cup, about 5 minutes. Put sauce in a small bowl; keep warm. Rinse and dry pan.
Lay bread slices, side by side, in a 10- by 15-inch pan. Broil about 6 inches from heat until toasted on both sides, about 3 minutes total. Keep toast warm.
Place frying pan over high heat; when very hot, add foie gras. Brown slices lightly, turning once, about 1 minute total (fat spatters, so partially cover pan). Take off heat.
Put toast on plates and top each slice with about 2 teaspoons of foie gras fat. Top equally with foie gras.
Drizzle warm sauce equally over foie gras. Season to taste with salt.
Nutritional analysis not including foie gras, which is approximately 98% fat.