Clean the crawfish.

Heat the butter (along with some crawfish butter) in a skillet, and sauté the minced shallots for 2 minutes, without browning them.

Add the cleaned crawfish tail meats and sauté for 3 or 4 minutes.

Add the white wine, salt, and pepper. Cook for 4 or 5 minutes.

With a slotted spoon, take out the crawfish, put them into a heated casserole, and cover.

Boil the liquid in the skillet until the volume is reduced by half.

Add the crème fraiche, bring to a new boil, and reduce until you have a thick sauce. Add some more salt if needed, and stir in a little cayenne (go easy on the cayenne unless you are on the frisky side or otherwise need some heat).

Pour the sauce over the crawfish and serve in the casserole, garnishing with the tarragon leaves.