According to Auguste Escoffier in his Guide Culinaire (pub 1903) darne means: "this is simply a large slice or cut, usually of salmon or other large fish." Of course, poisson means fish.
Charles Fellows in his The Culinary Handbook (pub 1904) defines darne as: "Name sometimes seen on a 'bills of fare'. It is a French word for slice, and is generally used in the term 'Darne de saumon' which is a salmon steak."
Jeff Smith (The Frugal Gourmet) in the updated and reprinted edition of Charles Fellow's original work The Frugal Gourmet's Culinary Handbook (pub 1991) says: "A darne is any thick slice of raw fish."
Since "transvere slice" and "cross slice" mean the same thing ... it's just a big slice of fish from dorsal to pectoral (top to bottom) - not head to tail.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain