Bring a large pot of salted water to a boil. Cook the fettuccine according to package directions; drain.
Meanwhile, put the bacon in a large, cold skillet, then cook over medium-high heat, stirring occasionally, until crispy, about 8 minutes; transfer to a plate with a slotted spoon.
Sprinkle the chicken lightly with salt and pepper and add to the skillet in a single layer. Let cook, undisturbed, until golden brown on the underside, 2 to 3 minutes. Continue to cook, stirring occasionally, until cooked through, about 4 minutes more. Transfer to the plate with the bacon.
Reduce the heat to medium and add the garlic, stirring, until fragrant, about 30 seconds. Add the tomatoes and cream and bring to a simmer, then add the spinach and stir until just wilted. Add the bacon, chicken, fettuccine and Parmesan and toss with tongs until well coated; season to taste with salt and pepper. Sprinkle with basil and serve.