The so-called "abbey" still stands in the courtyard we now call Caserne Feuquières (in honour of Manassès de Pas de Feuquières, an officer who was born in Saumur in 1590, his aunt was Charlotte Arbaleste who was married to Duplessis-Mornay). The abbey is what's left of the château's Saint-Florent monastery abbey, founded in the 10th century. The benedictine brotherhood left the site soon after 1024 to move to what is now Saint-Hilaire-Saint-Florent.
Saint-Florent Abbey has faded from memory but it was one of the biggest in Western France between the 10th and 16th century.
The abbey's rooms are currently not open to visitors.
If you'd like to find out more about the items on display at the Château-Museum, you can view the list of Museum pieces (Joconde database by the French Ministry of Culture)