We visited London and Paris in August for that amount of time and had a wonderful trip!
You could have 3 days in London and on the 4th day take the Eurostar from London to Paris and then have 3 days in Paris. In London you could see the Westminster area with Big Ben, Parliament, Westminster Abbey and the outside of Buckingham Palace. The Tower of London with the included beefeater Yeoman Warder tour is great and best done in the morning to see the Crown Jewels first. Seeing the Churchill War Rooms or one of the museums and having tea somewhere and shopping at Harrods is also fun.
In Paris I would recommend a Seine River Cruise soon after arrival and going to Trocadero to see the lights of the Eiffel Tower lit up at night. Our favorites in Paris are the Musee D'Orsay and the Louvre (especially the Napoleon III apartments there and hot chocolate at Angelina's in the Louvre for a break), We also enjoy strolling along the Champs Elysees and seeing the Arc d'Triomphe. The Luxembourg Gardens and St Germain area as well as Sacre Coeur and Montmartre are also great.
Get tickets in advance for the Eurostar as they get more expensive closer to the date you go. Also arrive 90 minutes before the Eurostar departure to go through security and immigration since the UK is not in the Schengen zone.
If you wish to have a more leisurely trip there is plenty to do in either London for a week with day trips to Windsor Castle or Hampton Court Palace, or a week in Paris with a day trip to Versailles.