Heat oil in a large skillet over medium heat. Add mushrooms and shallots; cook, stirring occasionally, until mushrooms are browned, about 6 minutes. Season with salt and pepper. Transfer mixture to a bowl.
Add wine and thyme sprigs to pan and bring to a simmer; cook 3 to 4 minutes, until reduced to about 1/2 cup. Whisk in crème fraîche, add mushrooms back to pan, and simmer mixture for 5 more minutes, until sauce is thickened and coats mushrooms. Remove thyme sprigs, and serve.