In a small saucepan boil wine and water with sugar until sugar dissolves, about 3 minutes, and remove pan from heat. Cool wine syrup slightly and chill. Wine syrup may be made 1 week ahead and chilled, covered.
Halve the figs and cut nectarines into thin wedges. In a bowl gently toss fruit with ham or prosciutto and half of wine syrup.
Arrange salad on a platter and pour remaining wine syrup over it. Garnish salad with mint and/or grape leaves.