Scrub the mussels, scraping off any barnacles and pulling away the beards. Discard any damaged shells or any open ones that don't close when tapped firmly with a knife or against the edge of the sink.
Melt the butter in a large saucepan. Add the shallots, garlic, coriander and thyme and fry very gently for 2 minutes. Remove from the heat and stir in the flour to make a thin paste. Gradually beat in the wine, using a whisk or wooden spoon, until smooth.
Return to the heat and cook, stirring, until the sauce is thick and smooth. Stir in the tarragon. Tip in the mussels and cover with a lid. Cook for about 5 minutes, shaking the pan frequently, until the shells have opened.
Drain the mussels to warmed shallow bowls, discarding any that remain closed.
Stir the cream into the sauce and bring to the boil. Season to taste and ladle the sauce over the mussels. Serve with warmed, crusty bread.