If you're flying into Paris, will your next country be England or Germany? If it's England, take the Eurostar train to London. Then, after your time in England, take a budget airline (easyjet, ryanair, others) to Frankfurt, and fly home from there. If you're going to Germany after France, then take a train or fly to Frankfurt, and, after your Germany time, fly to London, and when you're done fly home from London. Skyscanner can help you find these flights. Flying roundtrip from home to Paris and back home means you have to return to Paris at the end of your trip, which will cost you time and money unnecessarily.
With six days in each country, you won't have time to see much outside Paris and London. I'd suggest basing yourself in those capitals, and taking one or two day trips as time allows. In France, you could take a train to Chartres or Reims or Rouen or Giverny and see some countryside from the train, or you could rent a car for a day's drive with more flexibility. In England, you could take a train or a tour to Bath. The Cotswolds and Wales would be too far for day trips, I think. And renting a car in England means driving on the left, which takes getting used to. (I'm assuming that you live in a right-side-driving country.)
Rail passes don't usually work for trips like yours, with limited time and destinations. And you won't need advance reservations for most day trips by train from the big cities. Remember, the more time and money you spend moving from place to place, the less time and money you have to enjoy and experiences the places themselves. In the time you have, if it were my trip, I'd stick to the big cities.
Hope that helps.
