Preheat oven to 350 degrees F. Brush 1 side of baguette slices with 2 tablespoons oil and arrange, oiled sides up, on a baking sheet. Toast bread in middle of oven until golden on top, about 7 minutes, then transfer to a rack to cool. Leave oven on.
Stir together fresh and dried tomatoes, basil, vinegar, and 1/2 tablespoon oil. Spread each toast with tapenade and top with a slice of goat cheese and a rounded teaspoon of tomato mixture. Arrange tartines on a baking sheet, then season with salt and pepper and drizzle with 1/2 tablespoon oil.
Bake tartines in middle of oven until cheese is softened, about 5 minutes. Transfer to a platter and drizzle with remaining 1/2 tablespoon oil.
Toasts may be made 2 days ahead, cooled completely, and kept in an airtight container at room temperature.
Tomato mixture may be made 1 day ahead and chilled, covered
Recipe courtesy of Gourmet Magazine