My family and I plan to spend 14 days in Europe (not including flying in and out days), between London and Paris. Will be there in late June and early July, will have two teenagers with us. We will most likely be staying in London and Paris, but I would like to find one other location to stay that is easy to travel from either of these places. We will be flying in and out of London.
What interests you? Normandy is a short train ride from Paris. Lots of history as well as natural beauty, beaches, food. In the UK, while not between London and Paris, Bath or Salisbury are a short train ride away and that gives you access to Stonehenge,
In any case, to take the Eurostar between London and Paris, no matter where your third location is you have to go back to one of those cities to catch the Eurostar. There is no train service from Normandy to London, for example, although there is a ferry. Any chance you can fly into London and out of Oatis or vice versatility to save doubling back?
Normandy from Paris is a good suggestion. Or maybe Strasbourg - get a little taste of Alsace.
Strasbourg is a nice idea — easy to get to on the TGV and so beautiful in the summer with the geraniums spilling all over the gorgeous facades. Fun to take a river tour, and a totally different feel than London or Paris.
How about Windsor for a couple of nights either right when you arrive or just before you leave. Very close to Heathrow, so accessible. Great town, excellent castle, Eton is fun and interesting. Might work.