Preheat oven to 225 degrees F.
In a medium saucepan, combine fresh berries with 1/4 cup sugar and the water and bring to a simmer.
Cook over moderate heat , stirring occasionally, until the berries have softened and released their juices and the sugar has dissolved completely, about 8 minutes.
In a large bowl, whisk the eggs with the heavy cream, the remaining 3 tablespoons of sugar and the cinnamon, ginger and allspice.
Transfer the cream and egg mixture to a 9x13 baking dish.
Heat a large cast-iron griddle over moderate heat and lightly butter it.
Working in batches, dip half of the brioche slices in the cream and egg mixture, turning them once, until the slices are moistened but not soggy.
Transfer the soaked brioche slices to the griddle and cook them over moderate heat, turning once, until they are golden on both sides and cooked through, about 4 minutes.
Transfer the finished French toast to a baking sheet, cover loosely with foil and keep warm in the oven while you soak and cook the remaining brioche slices.
Transfer the French toast to plates and serve right away, accompanied by the warm berry compote and creme fraiche.