You can rent a car at Bordeaux-Merignac Airport or you might also opt to hire a taxi at the airport.
You can prebook a taxi with a car seat if required from Bordeaux Taxi Transfers. Alternatively,you can take a shuttle from the airport to the city centre and main railway station and can take the train from there. The bus runs every 45 minutes and costs €7.
Travelling by train is a useful way to see the region and french trains tend to be modern and reliable. Most stations are stroller accessible however, you may need to carry your stroller up or down a few steps in some areas. .For information about local (regional) trains in Aquitaine, visit http://www.ter.sncf.com/aquitaine/ which includes maps and printable timetables. This site is however only in French. There are also buses within the region and Eurolines run regular buses between the major towns and cities.
By far the best way to see the region is by car. For tips on driving in France and for car seat laws, click here. If you are staying in Bordeaux a car will not be necessary as the city is well serviced by bus and tram.