I can help you put together a good plan for less than that. I go to London and Paris all the time. Both are cities it is relatively easy to plan for. I also always recommend booking directly instead of with a third party. Too much shit can go wrong.
Feel free to message me. For a first time, I think 5-6 nights in both Paris and London are the right amount of time.
On Stonehenge, you cannot get close to it, unless you do a sunrise or sunset tour, and you need to put in for that NOW. You do that directly with English Heritage. https://www.english-heritage.org.uk/visit/places/stonehenge/things-to-do/stone-circle-access-visits/
On Normandy, I did this with my parents. We trained out to Caen, rented a car, drove to Mont Saint-Michel, then back to La Pointe du Hac. We did this in late November, so days were shorter, so in the summer, it should definitely be doable.
For flights, if you have flexility, look at Google flights. 6500 for 4 seems high, unless that is a mix or business/prem economy. For four coach flights, that is definitely high.
For where to stay, with two adults and two teenagers, I would look at AirBnB vs. hotels. You need more space. Some search tips, though. Always look for properties with a number of reviews. And preferably, you go for the AirBnB Superhosts. For both, you want to be relatively central. In London, I recommend Westminster, Bloomsbury, Holburn, or Farringdon. Those areas are central and will be less $$$ than Mayfair, Convent Garden, or Soho. Bermondsey, Southwark, and Islington are a little further out, but very cool to stay in.
In Paris, I usually stay in the 1st, but The 3rd, 5th and 6th are very, very good places as well. You can get better pricing if you are willing to go 9th, 10th, or 11th, and those areas are very, very cool. I also like the 14th and 15th, as there are areas that are very central, but also more residential areas so less $$$.