There is a very good collection of short trips put together in a book called an Hour Outside Paris; the author has put together, for those that lack a car but know Paris well, many of the interesting things to see just outside of Paris "intra muros". Here's a review: perhaps worth getting if you have a chance. http://www.francerevisited.com/main/node/194
If you are going to be here June 11/12, the 24 hours of Mans is on...and M3 GT2s will be running.
Have you been to Vincennes? Invalides (the military museum I imagine you have seen given your nom-de-plume). The Air and Space museum at Le Bourget is worthwhile...one of the best collections of aircraft and space platforms anywhere.
Other museums many don't have a chance to catch: Musee de Moyen Age, Musee Quai Branly, the Monet museum in the 16th (but check because their collection travels a lot). If you are coming with kids, the Cite de Science is fantastic and interesting for adults...there is a French attack sub suspended in a pit that you can go into and walk outside of.
PM me your dates and email/mobile and maybe we can try have a drink while you are here.