Cook the fettuccine according to the package directions. Drain and set aside.
Meanwhile, heat the oil in a large saucepan over medium-high heat. Add the onion and garlic and cook until the onion softens, 2 to 3 minutes.
Add the sausage and cook about 5 minutes, using a wooden spoon to crumble it.
Add the tomatoes and cook until the skins burst, about 8 minutes. Stir in the vinegar, salt, and pepper.
Add the cooked fettuccine, basil, and arugula and toss gently to combine. Serve in bowls and top with the Parmesan.