I have never planned a trip with 5 persons, but my Daughter and her family (2 adults, 2 teens, 2 pre-teens( did a drive tour of portions of France by renting a van of some kind and staying in B &Bs. They did not stay in Paris this time, since they had been there before. They visited Normandy and the Champaign and Alsance regions of France and loved the trip.
I have been to those places in France myself and loved it. The French countryside is great and not as expensive as Paris.
Consider Normandy (don't miss the Bayeux Tapestry and D-day beaches(, the Loire Valley and Alsance (near Germany)(perhaps you should skip Alsance since it is a bit out of the way in order to visit England as well.
For England, you can take some great day trips from London, or as someone recommended rent a car and drive the wonderful English countryside to visit, Salisbury, Stonehenge, Bath and the Cotswolds, which are south and west of London.