Wash the limes with hot water and pat dry. Grate the peel in a blender. Rinse the basil and shake dry. Pluck the leaves and add them to the blender with the sugar to add to the lime peel. Mix everything.
Wash and clean the strawberries and, depending on their size, cut them in half or into quarters. Marinate with Grand Marnier and arrange on plates. Spread the creme fraiche on top and sprinkle the basil-lime-sugar on top. Serve.