Drain the oil from the jar of sun-dried tomatoes and set the tomatoes aside.
Add the crushed tomatoes, Italian seasoning, and minced garlic to the slow cooker and stir to combine.
Stir the drained sun-dried tomatoes into the tomato mixture, then pour in the jar of alfredo sauce and mix until combined.
Place the chicken breasts on top of the sauce, pressing down lightly so they are just submerged.
Cover and cook on high for 2.5–3 hours or on low for 3–3.5 hours, until chicken is cooked through.
About 15 minutes before the sauce is ready, bring a large pot of salted water to a boil and cook the fettuccine according to package directions; drain.
Remove the chicken from the slow cooker and chop or shred into bite-sized pieces, then return the chicken to the sauce and stir to combine.
Stir the grated Parmesan into the sauce until incorporated, then toss the sauce with the cooked fettuccine to serve.
Optional: garnish with chopped parsley and additional Parmesan before serving.