The classic work is Robert Paxton's Vichy France: Old Guard and New Order 1940-44. It's an old work (1972) but a seminal one that laid down many of the key themes/arguments around Vichy, spelling out its fundamentally collaborationist nature and dispelling some persistent myths.

Most of Paxton's arguments are still valid today and are echoed in Julian Jackson's more recent (2003) France: the Dark Years 1940–1944. This is the latest 'definitive' work on Vichy in English and the one I'd advise to start with. I'm a fan of Jackson's and would also highly recommend Jackson's work on France in the 1930s.