The TGV from Paris to Poitiers takes between 1:30 to 1:50 h depending on the amount of stops. In Poitiers you can get around by bus (e.g. line 9 if you want to go to Parc du Futuroscope) or taxi. Numbered buses drive during the week, busses A, B, C and D during the weekend. In the city-center everything can be done by foot.
The TGV from paris to bordeaux passes through Poitiers and it only takes an hour and a half, so is brill! Also the auto-route runs nearby
Buses! Cheap, Frequent, and cover loads of routes!
Although generally, Poitiers is so small, you will reach everything you need by foot.