In a mixing bowl, combine cream cheese, honey, lemon zest, and 3 tablespoons of the basil. Whip on high speed until light and fluffy.
In a skillet, heat the olive oil on medium heat. Once hot, place each slice of French bread into the pan. Toast each side until golden brown.
Once toasted, spread each of the toasted bread slices with the whipped cream cheese mixture, about 1 tablespoon per slice. Divide the raspberries and blackberries between each of the slices and place on top of the cream cheese. Sprinkle each with the remaining basil.