Preheat a gas grill on medium-high, covered, for 10 minutes. Whisk together mustard, parsley, vinegar, olive oil and shallot in a small bowl and set aside.
Place potatoes and 1 tsp. salt in a large saucepan and cover with water. Bring to a boil, lower heat and simmer until potatoes are tender, 10 to 15 minutes. Drain and let cool slightly in a colander.
Turn grill down to medium. Prick sausages in a few places with a fork and grill, turning occasionally, until an instant-read thermometer inserted into middle of one registers 160°F, about 10 minutes. While sausages are cooking, cut each potato in half and transfer to a large, shallow bowl. Toss potatoes with dressing and serve immediately with sausages.