The problem arises because the dimensions of your image are square, while the projected dimensions of the bounding box are not (the rectangle you are asking to draw is more than twice as high than it is wide).
If you ask Mapnik (nik2img) to put a rectangle that is much higher than wide into a square output file, it will add stuff to the east and west that you haven't asked for. Actually nik2img should tell you the box it has decided to draw in `-v` mode. Read the output.
For a bbox of "4 51 6 54", you have to specify the dimensions "1500 3698" (or "500 1233") to get an image that exactly contains your bounding box.
See also the `--aspect-fix-mode` option of nik2img which allows you to control what happens when bounding box and image dimensions do not match.
If you want an output file that has the same aspect ration than as the bounding box in degrees (e.g. you enter a box that is 2 degrees wide and 2 degrees high and you want a square output file) then you have to choose `--srs 4326`.