Remove stalks from fennel. Mince 2 tsp. fronds; discard stalks. Cut fennel bulbs into quarters and remove core and any damaged outer leaves. Slice fennel crosswise into thin slices; transfer to a large bowl.
Cut off tops and bottoms of grapefruits. Slice off peel and white pith. Working over a bowl, cut between membranes to remove segments, dropping them into bowl. Squeeze membranes over bowl to extract juice. Using a slotted spoon, put segments in bowl with fennel, reserving juice; add onion.
Make dressing: Whisk 6 Tbsp. of reserved juice with garlic, mustard, tarragon and reserved 2 tsp. minced fennel fronds. Slowly whisk in olive oil and season with salt and pepper.
Toss arugula with 3 Tbsp. of dressing. Line a platter with arugula. Toss fennel mixture with remaining dressing and arrange on top of arugula.