Hard boil the eggs, then remove from the heat and peel. Mix the yogurt, crème fraîche, and lemon zest in a bowl. Season to taste with salt and pepper.
Rinse and quarter the pepper. Rinse the celery and pat dry. Rinse the tomatoes. Finely dice the vegetables. Mix the prepared vegetables and the crab into the yogurt mixture. Cover and let infuse in the refrigerator for 15 minutes.
Rinse the arugula, pat dry, and thinly slice the large leaves. Quarter the eggs. Gently mix the eggs and the arugula into the yogurt mixture, and serve.