Preheat oven to 350 degrees F. Lightly brush 12 slices of baguette with half of the olive oil and lay them directly on the middle rack of the oven. Toast for 5 minutes, or until light golden brown. Put the remaining olive oil in a small saute pan and warm over medium-high. Add the grapes and saute for 2 to 3 minutes or until soft and warmed through. Remove from the heat. Sprinkle the balsamic vinegar over the grapes and add a few grindings of pepper.
Top each baguette slice with one leaf of basil and spread the goat cheese evenly among the toasted slices. Cut each slice of prosciutto in half and drape over the cheese. Top each of the baguettes with three of the sauteed grapes.
May be served warm or made in advance and served at room temperature.