Bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente. Reserve ½ cup of pasta water, then drain.
Season the salmon fillets with salt and black pepper. Heat 1 tablespoon of olive oil in a large skillet over medium heat. Cook the salmon for 3–4 minutes per side until just cooked through. Remove from the skillet and set aside.
Add the remaining olive oil to the same skillet. Add the sage leaves and garlic and sauté for 1–2 minutes until fragrant and the sage is lightly crisp.
Add the cooked pasta to the skillet along with lemon juice, lemon zest, and a splash of reserved pasta water. Toss gently to coat.
Flake the salmon into large pieces and add it to the pasta. Toss gently to combine.
Remove from heat and sprinkle with Parmesan cheese and red pepper flakes if using. Taste and adjust seasoning before serving.