Heat oil and butter in a medium skillet of medium. Cook shallot and garlic, stirring often until soft and golden, about 4 minutes. Add in creme fraiche and cook until mixture is slightly thickened, about 3 minutes.
Meanwhile cook the pasta in a pot of boiling salted water, stirring occasionally until very al dente (about three minutes for fresh pasta).
Using tongs, transfer pasta to skillet with sauce and crabmeat. Finely grate zest from lemon over the pasta and squeeze in about 1 tsp. juice. Cook pasta, tossing constantly and thinning sauce with a few tablespoons of the pasta cooking water if needed until pasta is glossy and sauce is the consistency of heavy cream, about 3 minutes. Add tarragon, season with salt and toss a few more times to wilt tarragon.
Transfer pasta to bowls and sprinkle with crushed red pepper.