Filet Mignon (French for dainty fillet) is the most tender cut of meat. It tends to be quite expensive. It is usually grilled, broiled, pan fried, or roasted. It is often larded with bacon to increase the fat content. Take my advice, enjoy this cut rare with a fine bottle of wine.
In addition to the wines mentioned in our food pairing table you might consider a fine French Bordeaux wine or a high-quality Cabernet Sauvignon or Pinot Noir.