This has been called the most expensive omelette in the world, which it may be at 35 Euros if you get it at its birthplace in the shadow of the imposing Mont St-Michel on a little island off Normandy. There's some lore about it that seems to be more a matter of effective marketing than of actual tradition.
So what is it? It's a very fluffy omelet with nothing else. Much has been written about how to achieve the proper fluffiness, but the official recipe is a secret of that restaurant and the various attempts that you see online cover a wide range of efforts.
From what I can pull together from the history, a brief description by Mere Annette Poulard herself, the many articles about it, and my own attempts, I think I have something that is very close to what she would have served in her little kitchen in 19th century Normandy.