I call it a Chesterfield. At least that style with a straight back is; I don't know if the swooping back changes the style.

I've linked some images below -

Here is a link that might be useful: Images of chesterfield sofas

I would also call it a Chestefield.

Curved back Chesterfield.

ML

It's a tufted meridienne. Some meridiennes have only one arm, some have asymmetrical arms and back.

Chesterfields have even arms and back.

This post was edited by palimpsest on Sat, Aug 16, 14 at 13:29

Well, who wins the bet?

Kind of think we both lost, but I came closer. He said Chesterfield; I said emphatically not, maybe French rococo and recamier mixed together.

Edited to add:
Heartfelt thanks to all who contributed to the solution. ;)

This post was edited by kitchendetective on Sat, Aug 16, 14 at 15:43