In a large bowl, combine the fennel, apple, carrots and raisins to make the slaw. Drizzle with olive oil, cover and refrigerate while preparing remaining ingredients.
In a small saucepan, mix together the sugar and apple juice. Place over medium heat and cook until reduced to about 1/4 cup, about 10 minutes. Remove from the heat and cool. Stir in the apple cider vinegar. Pour the apple juice mixture over the slaw and stir to combine well.
Chill thoroughly. Serve on lettuce leaves.