Remove roots, outer leaves, and tops from leeks, leaving 1 1/2 to 2 inches of dark leaves. Slice leeks in half lengthwise; rinse with cold water. Drain. Remove dark leaves; chop dark leaves to measure 1 1/2 cups; set aside. Chop bulb ends to measure 2 cups; set aside.
Remove stalks from fennel bulb. Chop the stalks to measure 1 1/2 cups; set aside. Chop bulb to measure 2 cups; set aside.
Combine chopped dark leek leaves, chopped fennel stalks, 5 cups water, wine, and fennel seeds in a large Dutch oven; bring to a boil. Reduce heat; simmer 25 minutes. Strain leek mixture through a sieve over a bowl, reserving stock; discard solids.
While the vegetable mixture simmers, combine 8 cups water and lemon juice. Working with 1 artichoke at a time, cut off stem to within 1 inch of base; peel stem. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom. Cut artichoke in half lengthwise. Remove fuzzy thistle from bottom with a spoon. Cut artichoke lengthwise into quarters; place in lemon water. Repeat procedure with remaining artichokes.
Drain artichokes; discard lemon water. Heat oil in pan over medium heat. Add chopped leek bulbs, salt, and pepper; sauté 5 minutes. Add garlic; sauté 2 minutes. Stir in chopped fennel bulb, artichoke quarters, reserved stock, potato, chickpeas, tomatoes, and saffron; bring to a boil. Cover, reduce heat, and simmer 35 minutes or until vegetables are tender. Serve with Rouille.