Prepare a medium-hot fire in your grill. Then place the peach halves cut-side down. Grill for 4 to 6 minutes, turning once, until the peaches are tender and blistered.
Transfer the peaches to a work surface, like a clean cutting board. Remove the skins, cut the peaches into thin slices, and place in a medium bowl. Sprinkle with sugar and a squeeze of lemon juice, and toss to blend.
Grill the brioche slices for 1 to 2 minutes per side, or until they have grill marks. Meanwhile, stir the honey into the yogurt.
To serve, place each brioche slice on a plate. Top with peaches, raspberries, and a dollop of honeyed Greek yogurt.