Yes, this is a problem. Could you spray the base of the fencing with weedkiller to keep the weeds down? It may look a bit brown but may be better than weeds. Could you plant a hedge on the inside of the fence with a path between the hedge and the fence? This would allow you to spray off the weeds regularly and would hide the 'mess'. It depends how much space you have. The hedge could be an informal row of mxed shrubs.

Could you clothe the fence with climbers? I also have a rabbit fence which I only put up last year so it's still horribly new, but I'm growing variegated ivy on it in the shade and honeysuckle, passionflower and clematis on it in the sun. A friend also suggested a vine for the sunny side.

good ideas many thanks

maybe a raised planter but put a membrane at the bottom and make sure you have it quite deep and dont plant huge trees or shrubs.