Bring a large pot of salted water to a boil over medium-high heat. Stir in the penne. Decrease the heat to medium-low and cook, stirring occasionally, until tender but firm.
Meanwhile, put the tomatoes, basil, garlic, fines herbes, salt, and pepper in a bowl large enough to also accommodate the cooked penne. Stir gently until well combined. Drizzle in 1 tablespoon of the oil and stir gently until the tomatoes are evenly coated. Coarsely chop the arugula (rocket) and put it on top of the tomato mixture. Chop the artichoke hearts and put them in a small bowl.
Drain the penne well and, while it is still piping hot, pour it over the tomato mixture. Drizzle with the remaining tablespoon of oil and toss gently until thoroughly combined. Gently stir in the artichoke hearts. Serve immediately.
Note: The tomato mixture and artichokes may be prepared up to 4 hours in advance. Just store them separately in covered bowls in the refrigerator.