Clean and wash the fennel and put the fennel green aside. Cut the fennel into very thin slices. Mix with vinegar, salt, pepper and oil.
In the meantime, place the bacon in an aluminium grill tray and fry until crispy on a hot grill or in a hot grill pan. Take out and let it drip off on kitchen paper.
Cut the melon skin from the flesh. Cut the fruit flesh into 4 large pieces. Grill on the hot grill for about 3 minutes while turning. Arrange melon and fennel on plates. Crumble the bacon coarsely and sprinkle with the fennel green over it.