We often start a trip to a new city (when we are still a bit jet-lagged and disoriented) by doing one of those hop-on hop-off bus tours. Great way to get a feel of the layout and distances of the city and have an introduction. Most of the companies give you a second day for free or heavily discounted. We did this in Paris, and it included a boat tour as well.
My favorite place to visit in Paris was Sainte-Chapelle.
Instead of the hop on hop off bus, I recommend fat tire bike tours. Teenagers don’t want to sit on a bus. We had so much fun we did both the day and evening tour.
Haven’t been on the bike tour mentioned by @Momtogirls but we’re like @college_query and have numerous times gone on the hop on hop off busses when jet-lagged but arrive in a city too early to have dinner and go to bed. We get a general lay of the land and, depending on energy level, get off and see a few of the sites. The second day is a bonus that you can use for the sites you didn’t see the day before or you can sightsee on your own.
A good arrival day activity in Paris is a boat cruise on the Seine. Nighttime is a great time to go. You’ll get an overview and it is good for jet-lagged bodies.
How many days and nights?
Day trips from Paris:
Strasbourg - a very pretty city in the Alsace region
Normandy Beaches (a very long day, van tours leave from Paris)
Versailles
Chartres
Giverny (Monet’s gardens, but dependent on weather. Nice bike tours available)
Various Chateaux
I could (and have) spend weeks in Paris and still not see it all.
Head to the library and check out some guidebooks or find them on line. I like the eyewitness guides, but there are plenty of specialty guides and day trip books out there.
We always plan a lot of walking on our first day - keeps us awake and exposure to sunlight will help reset your circadian rhythm.
Rick Steves has some fabulous audio tours of museums but also of neighborhoods and historic areas in many European cities. I believe there is one titled “historic Paris walk” or something like that. Best of all, they are free! Just have everyone download the app on their smartphone then search for the audio tours that interest you. Oh, and don’t forget your headphones 
I agree with the idea of staying in France…since you are outdoorsy types I would vote for some the day trips outside of Paris.
If you are adventurous with regards to your accomodations I recommend looking on www.sawdays.co.uk or Google Sawdays special places to stay in the UK, France, Spain. Want to stay in a castle, a country manor, a thatched cottage, a carvan, a tree-house, or an elegant urban inn? They have it all. I’ve never used it (just drooled) but I referred my neighbors going to France and Spain last summer and they had a great experence at a Sawdays-listed B& B.
Wow! So much great advice. Interesting that several of you said hop on hop off bus tours. I’ll have to look into the bike tours as well.
It does make sense to do a walking tour that first day.
Holy cow @inthegarden! I will definitely look into it.
We spent a week in London and then a week in Paris and it still was not enough. While we were in Paris we took a day trip tour to the Normandy beaches. Very moving and worthwhile. You can also do day trips to Guerveny and Versailles. There is so much to do in and around those cities we decided we really need to go back.
All are fantastic locations but not crammed into one week. Stick with Paris and London at the most.
Since you are flying in and out of Paris and won’t gave much time, I agree with everyone to stick with France and mostly see Paris. If you really must see London too, there’s the Chunnel or flights but that eats up precious time that you will spend traveling.
If you have a couple of days you can visit Avignon - less than 3 hrs on TGV. Weather will be better there.
Great advice above. I would second/third/forth Paris as the base. Save London and other spots for another trip.
Even after multiple trips to Paris throughout my life (started as a college age backpacker), the last trip I took was 8 nights at one hotel with day trips to Giverny and Chantilly. I traveled with a girlfriend who studied there and lived in Paris for a number of years. We barely scratched the surface of all that we wanted to enjoy - and not everything was a repeat for either of us.
We did the same trip for Spring Break— our D was 18 and S was 16. Spent the entire week in Paris. (They are in their 20’s now and working.) It was a great trip, and I have wonderful memories of this last time that the 4 of us were together before D headed for college. You will treasure the memories.
My recommendation: Stay in Paris the entire time. Do day trips (Giverny, Versailles, Reims) if you want to explore more. Rent an apartment. They are a better value in Paris than hotels, and you will appreciate the space. Paris Perfect is a well respected agency, as are others.
Best memories: boat cruise on the Seine first day, dinner at Le Ciel de Paris (view of Eiffel), shopping with D at Galleries Lafayette and Printemps, Segway Tour, grocery shopping on Rue Cler and cooking in our apartment, wonderful guided tour at Musee D’Orsay, ALL of the incredible museums. I could go on!
Have fun planning!
If you don’t think you’ll ever get back–do Paris and London.
But otherwise try to minimize your traveling time and really enjoy your stay–there is so much to do and see and experience. You won’t fit it all in no matter what you do!
We spent a week in Paris and it wasn’t nearly enough time! I want to go back…
I recommend staying in an apartment. It will make it really special and you can do fun food shopping in the bakeries, cheese stores, outdoor markets, etc. it’s much easier to recharge and rest in an apt and you can get up early and enjoy your coffee and croissants without waking the teenagers. Save money on breakfasts and snacks
First time, maybe an apt with a view of Eiffel Tower or other landmarks
You could spend a day walking around the garden of Versailles. If you are there on March 31, go see the fountains. http://en.chateauversailles.fr/news/shows/fountains-shows-and-musical-gardens
You might do an overnight for the Normandy Beaches. My favorite was Pointe du Hoc. You can see the remains of bunkers there. Also see the Bayeux Tapestry depicting the Norman conquest of England in embroidery in the same general area. https://en.wikipedia.org/wiki/Bayeux_Tapestry
A bit more of trek is to go on to Mont St. Michelle.
Have ice cream at Berthillon’s it’s the best in the world. http://www.berthillon.fr/ It’s on the Ile St. Louis, so you can combine it with a trip to see Sainte-Chapelle a stained glass jewel. It was my then six year old’s son favorite site when we took him to Paris many eons ago. http://www.sainte-chapelle.fr/en/
I would just do France, with some day trips outside Paris proper.
I’m also very fond of the Carnavelet museum. http://www.carnavalet.paris.fr/en/museum-carnavalet
Honestly I wouldn’t leave France.
I’ve also been to Paris multiple times and wouldn’t even bother trying to fit in London on a one week trip. Part of the fun is “settling in,” i.e., walking some of the same routes or visitng the same bakery or local street market a few mornings. Feel like you belong. And yes, definitely look into renting an apt. You can cook some meals, don’t get interrupted by the maids. But if you feel you need to guidance/help of hotel staff, then that’s fine, too.
Not all museums are open every day. Just coordinating some of the what you can see when will take up some of the time. Frankly, I’d skip the Normandy sites, unless someone has a driving interest in that. Go see a nearby chateau, Versailles, maybe Chartres, you can do Berthillon after having crepes outside Notre Dame.
I think you’ll be glad not to spend time on long distance transport to other Euro countries.