Cook the pasta according to the package instructions.
Heat the olive oil and the butter together in a saute pan over medium-high heat. Stir in the shallots and garlic, and saute until they are light brown. Add in the thyme and mushrooms, and saute until the mushrooms are golden brown.
Deglaze the pan with the white wine, stirring to bring all the flavors together. Pour in the cream, and stir to combine. Allow the sauce to reduce until it becomes thick and coats the back of a spoon. Add the spinach to the cream, and toss together to coat evenly.
Once the pasta has cooked, drain the water, and transfer the fettuccini to the sauce. Toss the pasta and the spinach sauce together. Sprinkle in the fresh chives, and season with salt, and pepper, to taste. Remove the pan from the heat, and serve the fettucini in warmed pasta bowls.