Hey Shanti! I would definitely take the train into the city. I remember walking around certain parts of Paris and being in complete awe that there wasn't a massive pile-up accident! Unless, you've driven NYC for years, I'd say stick to public transit! The nice thing about Paris is that the Metro and your feet can get you just about anywhere in a decent amount of time.
As for places to see, I'd say a huge part of it depends on the age of your children. Another great factor is your budget.
I'm actually headed to Paris this summer with my soon-to-be hubby; I've been and he hasn't. I'm seriously considering doing one of the free -- yes, FREE -- NEW Europe walking tours. Eight years ago (at a 20-year-old), I did the NEW Europe free walking tour in Berlin. It was by far one of the highlights of my trip! The tour guides were young, energetic, knowledgeable, and entertaining! I learned a lot, saw a lot, and completely enjoyed myself! Anyhow, having had such an incredible experience on the tour, I figure its worthwhile doing in Paris. The tour in Paris hits a lot of big tourist sites: http://www.newparistours.com/daily-tours/paris-free-tour.html
On my last trip, I also did a day trip to Normandy and did one of the guided Normandy tours. This was another major highlight of my experience, and I feel like it would appeal to kids who are in middle or high school (maybe late elementary depending on their interests and demeanor). I did a tour through Victory Tours: http://lignerolles.homestead.com/ The fellow who runs the tours is a true history fanatic and does an incredible job of educating and entertaining. He also takes you to a lot of "off the beaten path" stops. While he is my number one recommendation, there are a variety of other Normandy tours available. Heading out to Normandy is definitely an all-day trip, and might require a bit of planning with public transportation.
On this upcoming trip, my fiance and I are looking at traveling to Versailles. We are going to create our own tour this time! Trying to keep the budget down.
Paris is one of those places, where there are far too many places to see! I think the walking tour will give you a good feel for the city, and also give you ideas as to what you might want to explore in the following days with your family. Also, try doing a picnic in the parks near the Eiffel. Grab some bread, cheeses, and maybe some meats (or wine for the adults) from the shops near your hotel, and picnic under or near the tower. My girlfriends and I did that instead of waiting in line to travel up the Eiffel. Far more fun, and you got to pop in French shops and experience French culture in preparation.
Oh! And before you go, try to learn just a few phrases in French. The French really appreciate when tourists at least attempt to speak the lingo!
