First of all, unless it is absolutely necessary, I would strongly suggest that you avoid checked baggage. Most of our trips to Europe last year involved reroutings (and once an unexpected overnight stay in LA) along the way and we were very glad to have our baggage with us. Without fail we merely whizzed through customs and were on the train to town while the masses were standing around awaiting the arrival of their bags. Additionally, minimal luggage certainly makes navigation within Paris far easiser.
The trains are great and can speed you from point to point within the city in a mere fraction of the time it would take via taxi, but you do need to be able to handle your own luggage in some cases up and down several flights of stairs.
A careful planner can easily pack a two week wardrobe into a carry-on, simply washing lingerie and tops along the way. I find that silk, knit tops are great for travel as they dry fairly quickly, are very versatile and don't require any ironing.
With a black jacket, one black knit skirt, one pair of black knit pants and several tops and scarves, I can go almost forever, and, if I run short, they do sell clothes in Paris.

One can always buy another bag and check it on the way home when you really don't care if it gets delivered in a few days.