What is the best way to cook the beef cut "nerveux gite"?

Welcome! Braising would be the preferred cooking method for that cut of beef. The long, slow cook will result in falling apart, tender, moist meat.

Because of the name of the cut, the first thing that comes to mind is beef bourguignon. From Wikipedia :

It is a stew prepared with beef braised in red wine, traditionally red Burgundy, and beef broth, generally flavoured with garlic, onions and a bouquet garni, with pearl onions and mushrooms added towards the end of cooking.

If you decide to make beef bourguignon you can do a search to decide on a recipe. Julia Child's version is quite famous.

However, the bottom line is that you want to braise the beef. So you could use it in any recipe where braising is the cooking method called for.

I would allow 2-3 days total time to realize the full beauty of this beef cut. And I'm jealous of you, they know this cut in France. We call it beef shank in the U.S. and it's not easy to find. The bone and marrow are what make it taste so good. And I can tell you that I know Mexican cooks who make this into glorious dishes like Caldo de Res, and some of the taco trucks make braised beef tacos using beef shank. You can't screw it up. Chop onions, celery, carrots, whole garlic. Season the heck out of the beef, sear it and then put it in a roasting pan or crock pot with the veg, cover with tomatoes and water and cook low and slow for 12-14 hours. Cool it, pull apart and reheat for tacos.

For tacos: Heat up some tortillas. Garnish: chopped onion, cilantro, jalapeños, lime and plenty of beer. Hot sauces and radishes on the side.