Light a grill or preheat a grill pan over medium-high heat. Clean and oil the grill grates or grill pan.
Slice the baguette in half lengthwise and brush the cut sides with a little oil. Sprinkle with salt and pepper.
Place the grapes with their stems still attached in a medium bowl. Coat the grapes with a little oil. Season with salt and pepper.
Brush the brie with a little oil, as well.
Once the grill is heated, grill the bread until charred on both sides, 3 to 5 minutes per side. Remove and slice into pieces.
Add the grape bunches to the grill and cook, turning every couple of minutes, until some of them begin to burst and they turn golden in color, 8 to 10 minutes. About 5 minutes before the grapes are done, add the brie to the grill.
If using two 8-ounce wheels of brie, grill until you see nice grill marks, 1 to 2 minutes per side. If using one 16-ounce wheel of brie, grill until you see nice grill marks, 2 to 3 minutes per side.
Remove the grilled grapes and brie and arrange on a board or platter along with the grilled bread.
Slather a little of the gooey, grilled brie on a piece of bread and top with a couple of the grilled grapes picked from the stem.