For the remoulade: whisk together mustard, paprika, Tabasco, salt and pepper. Beat in the vinegar and then, whisking constantly, add the oil in a slow, thin stream, continuing to beat until the sauce is thick and smooth.
Stir in scallions, celery and parsley and mix well. Cover the bowl and let the sauce stand for at least 2 hours before serving to allow flavours to blend.
To serve: pour the remoulade over the crayfish and roughly mix with the arugula leaves.