Wash the meat and dab dry. Clean and wash the fennel. Put some green aside. Cut the fennel into slices. Heat oil in a coated pan. Brown the meat on both sides, remove and season with salt and pepper.
Add the fennel to the pan and pour in the broth. Place the chicken filet on the fennel vegetables and cook everything for about 10 minutes. Season to taste with lime juice. Remove meat from the pan and cut into slices.
Alternate with the fennel slices on a plate. Garnish with fennel greens and lime slices. Pour broth around the meat. Sprinkle everything with pink berries. Serve with baguette.