You have info on the train station of Blois
from Paris gare d’Austerlitz is direct, then you can come by Paris gare Montparnasse, TGV Paris - Vendôme, then vendôme - Blois is 30 km or Saint-Pierre-des-Corps near Tours
for buses around and in Blois ,the TUB
the regional bus service TLC
again I come by car on the A10 sortie exit Blois, parking underground Chateau handle by Vinci or around the garden on the side of the castle=chateau at quai de la saussaye
a huge agglo including blois to improve public transport call Agglopolys ,see it in French
And local support to improve connections with Paris, bloisparisillico site here in French
As we could only rely on trains and public transport, even private companies, we had to find a way to get to the castle.
For those interested, there were -and I expecte still are- bus companies departing right from Blois station to Chambord and to another castle, one that inspired Herg?, and included it in a Tintin adventure.
We weren't much interested in the second one, so much that I don't even remember the name.