A battery cell arrangement having a battery cell which is in the form of a film cell and includes a flat cell body with two end faces, a flexible cell rim surrounding the cell body, and two contact sections arranged on a rim side of the battery cell. The battery cell arrangement further has a frame arrangement which includes a first frame element and a second frame element which frames the cell body on all sides on the rim. At least one vent opening is provided on a side of the frame arrangement which faces away from the end faces of the cell body, in order to allow fluid, in particular gas, to emerge from the battery cell arrangement in the event of damage.