Bring a large pot of salted water to a boil. Add the crab and cook for 13 minutes. Drain and let cool. Lift the carapace and clean the crab of all the “butter” and “lungs” inside. Break the crab in half. Separate the legs from the body and crack them open. Extract all the leg meat carefully; try to keep it intact.
Next, split the body and pick out all its meat. Go through all the crabmeat after it is picked to remove any stray shell fragments. Set the crabmeat aside in the refrigerator.
Remove any tough stems from the watercress. Wash and dry it well.
Peel and finely dice the shallots.
Carefully peel the zest from the lemons with a sharp vegetable peeler, being sure to take only the yellow peel and none of bitter white pith. If you do end up with some pith, pare it away with a sharp paring knife. Cut the pieces of zest crosswise into a julienne and combine with the shallots in a small bowl. Season generously with salt and freshly ground pepper.
Squeeze the lemons and add about 5 tablespoons of the juice to the bowl with the shallots and lemon zest. Add the Champagne vinegar, mix well, and let sit for at least ½ hour to macerate. Whisk in the olive oil; taste for salt, pepper, and acid and adjust as needed.
When you are ready to serve the salad, remove any blemished outer leaves from the endives. Cut them in half lengthwise and remove the cores, then cut lengthwise into strips. Put them in a serving bowl with the watercress, crab, and vinaigrette and toss well. Arrange on a platter or individual plates and serve immediately.