We will be arriving 2 days ahead of our tour start time/date. I figure the first day will be getting used to the time change, the hotel, etc... Then we have 1 full day and then a half day (till 3pm) on our own until our tour begins. Our tour won't include a tour of the Eiffel Tower - so we're looking into that with fattiretours.com. What else should we/could we see that isn't on the 7 Day Paris rick steves tour? Our tour is June into July, fyi.
There will be literally hundreds of guidebooks for Paris and the number of websites dedicated to the city won't be less. This is an global introduction from which you can make your own choice: http://en.parisinfo.com/discovering-paris/themed-guides/citybreak-a-paris
If you're a fan of Monet, you could visit the Marmatton museum - it's wonderful! Simply strolling around the many gardens and by the river will be nice too - a great way to get over jetlag.
If St. Denis Basilica is not on the tour, this is the most overlooked fabulous tourist site in Paris and is reachable on the metro (although slightly outside Paris) Here is one of our trips so you can see if it appeals to you: https://janettravels.wordpress.com/2010/10/26/confronting-mortality-at-st-denis/
This is the oldest Gothic church in Europe and the site of burial of the Kings of France.
There are lots of small interesting museums like Nissim Camondo and Jacquemart Andre and the Marmottan is a good choice. You don't say WHEN but if in spring summer or early fall then the Albert Kahn Museum gardens (at the Bologne St. Cloud metro stop on the #10 metro or the Promenade Plantee gardens on the abandoned elevated train tracks behind the Bastille Opera House -- or just hang in the gardens of central Paris like the Tuilleries or Luxembourg Gardens.
Since you'll be in busy Paris for 7 days, consider doing one of Rick's day trips in the Paris book.
I've done that tour and it is terrific! If you are staying near the Eiffel Tower, walk over there the first afternoon when you arrive. Then, you are right, I would schedule a tour for the next day. I would also consider doing Napoleon's Tomb and the Army Museum or the Arc de Triomphe altho both of those are covered by the Museum Pass you will get on the tour. If you have an interest you could also consider Pere Lachaise Cemetery. Notre Dame is also a consideration. The cathedral itself is free and altho there is a line it goes fast because it is just a matter of going thru 2 doors which slows everyone down on entry. (We did not actually go IN the cathedral during the tour but the guide did take us there and talked about the building, the statues on the outside, etc). The ND tower tour is covered by the museum pass and is a pay site, so you might wait on that. You could consider going to St Sulpice which is not covered by the tour. It also is free and very interesting. (Did you read Dan Brown's DaVinci Code? St Sulpice figures in that but I understand his portrayal of the features in the church are incorrect.) Marmottan is a wonderful suggestion if you have any interest in Monet and the Impressionist painters.
I also suggest walking along the Seine. Depending on where you are staying, to me it's a nice walk from the Notre Dame area to the Rue Cler area. I did it twice this last October when I was there and the weather was beautiful. Really, there is SO much to look at!
You will have NO trouble filling your time.
As the tour includes Paris Museum Pass, I would look at places not covered by the pass ...
--Marmottan Museum - Monet
--Carnavalet Museum (free) - Paris social history
On all of the 13 RS tours I have taken, I have always received a packet of information from the RS folks that includes a list of things that will not be included on the tour. As a disclaimer, I have never taken a 7 day RS tour. I would e-mail (or call) the RS travel desk and ask them if they will be sending you such information prior to your tour. We always arrive at the city the tours begin in several day ahead of time like you are planning on doing and then we go visit things that are not included on the tour that interest us. We were in Paris in both June and July of this year where we have stayed several times and there is so much to see and do in that city, we have never run out of things to visit. I would also recommend getting a RS Paris Guide Book if you have not gotten one already, even thou you will probably be getting some kind of book for your tour. A wealth of information that we use every time we visit Paris. Happy travels.
You don't have to wait for the RS office to send you suggestions on what to see before your tour - it's on this website. On this link, click the "Pre Tour" tab, and scroll down to "Sightseeing on Your Own": https://www.ricksteves.com/tours/france/paris#
Another thing not included in the Museum Pass that doesn't seem to be on your tour is the Jacquemart-André Museum (full disclosure - I've never been, but it's on my list for next time on a non-pass day).