Preheat the oven to 400°F. On the stovetop, heat a heavy-duty metal lasagna pan over medium heat.
Add the spinach and keep turning it over with tongs until just wilted, about 2 minutes. Remove spinach from the pan and set aside to cool; squeeze out excess water and chop finely. In the same pan, heat the olive oil over medium heat. Add the garlic and stir until fragrant but not brown, about 1 minute. Add the chopped tomatoes and cook over a gentle heat for about 25 minutes, until the tomatoes break apart and become saucy. Remove the pan from the heat, add half of the basil leaves and season to taste with salt and pepper.
Scoop out ½ cup of sauce and reserve. Spread the remaining sauce evenly over the bottom of the pan. In a large bowl, stir together the mozzarella, ricotta, artichokes, ½ cup Parmesan, spinach, zest, oregano, salt, pepper and remaining basil. Cut the lasagna sheets in half so that you have 12 pieces, each 5" x 6". Put about 3 tablespoons of filling along the bottom of the lasagna sheet and roll up to make a 1½" log. Place the cannelloni, seam side down, in the pan on top of the tomato sauce. Repeat with remaining lasagna sheets and filling, placing them close together in the pan. Mix the crème fraîche with 2 tablespoons of water to loosen it; pour over the cannelloni, being sure to cover all the pasta. Sprinkle with the remaining Parmesan.
Spoon the reserved tomato sauce over the cannelloni. Bake for 30 minutes, until the top is bubbling.