Heat broiler. Brush both sides of baguette slices with oil; place on a rimmed baking sheet. Broil until golden, 1 to 2 minutes per side; set toasts aside.
In a small saucepan, combine figs, sugar, wine, thyme, and a pinch of salt. Bring to a boil; reduce to a simmer, and cook until thickened, 7 to 9 minutes. Let compote cool to room temperature.
Dividing evenly, spread each toast with goat cheese, and top with compote. Garnish with drizzled honey and chopped walnuts.