In a medium saucepan, bring wine and 1/3 cup sugar to a boil. Cook, stirring occasionally, until slightly syrupy, 6 to 8 minutes. Remove from heat and stir in nectarines.
In a large baking dish, whisk together eggs, half-and-half, 2 tablespoons sugar, and a pinch of salt. Place bread in dish and let stand about 1 minute, pressing to help it absorb the custard; turn over and repeat.
In a large nonstick skillet, melt 1 tablespoon butter over medium; swirl pan to coat. Add 1/2 the bread and cook until golden, about 3 minutes per side. Transfer to a plate and repeat with remaining butter and bread. Serve topped with red-wine nectarines and ice cream.