Fill a large pot with lightly salted and oiled water and bring to a rolling boil. Stir in the fettuccine, bring back to a boil, and cook pasta over medium heat until cooked through but still firm to the bite, about 8 minutes. Drain and transfer to a serving bowl.
Pour cream into a skillet and bring to a boil; reduce heat to low. Add butter to cream and stir until butter is melted. Add Parmesan cheese to cream mixture and bring to a simmer until sauce is reduced and thickened, 5 to 10 minutes.
Mix peaches into sauce and cook until peaches are warmed, 2 to 3 minutes. Pour peach sauce over pasta and toss.