Bring a large pot of heavily salted water to a boil over medium-high heat.
While the water is coming to a boil, add peas to the pan. Heat butter in a large sauté pan and morels and peas. Cook until peas are barely tender (but not too soft or mushy), 3 to 4 minutes. Stir in garlic and cook 1 minute more. Season with salt and pepper.
Drop pasta into boiling water and cook until al dente. Drain well and transfer pasta to a large bowl. Immediately toss pasta with peas and morels, crème fraîche and basil. Season with salt and pepper to taste. Add more crème fraîche and basil if desired.