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There are two stations in Poitiers where TGV stop: Poitiers (the downtown train station), and Futuroscope. Some trains from Paris only stop at downtown Poitiers, others stop at Futuroscope on the way.
Futuroscope is served by line 1 (Monday to Saturday), line 1E (1 express, Monday to Friday), and line E (Sundays and public holidays). From the Futuroscope TGV station, it's a short walk. From the city, take the bus. There are 11 stops around the site, select the one that's closest to where you're going. On the way to the Futuroscope, all three lines have “Futuroscope” in their destination. The website seems to be currently broken, I can't access the schedules. You can get schedules for your day of travel from the interactive trip planner. For the train station in Poitiers, use Gare SNCF (Poitiers).
You can buy a bus ticket from the driver, in cash (1.30€). Exact change is recommended but drivers will give back change if they can. The ticket is valid for 1 hour. You can also buy a ticket from the regional ticket machine in the station. If traveling with other people, you can buy 5 tickets for a slightly reduced price (5.20€) from the machine in the station. There's also a day ticket valid for up to 4 people traveling together, which is cheaper for as few as 2 people making a return trip within the day (3.80€), but it isn't for sale at the station vending machine: you have to find a ticket agent (there is one outside the station: exit to the east (right side when coming from Paris) and cross Boulevard du Grand Cerf to bar-tabac Le Printania at number 139).
If you're standing at a bus stop and your bus is coming, signal the driver by waving your arm. Press the “stop requested” (“arrêt demandé”) a little before the bus reaches your destination stop.