Unfortunately a lot of monuments/castles in France suffer from that feeling of emptiness; I assume they were cleared out during the revolution. Your best chance of seeing interesting things as well as interesting buildings seems to be to look for privately-owned/smaller castles that are open to the public. I went to a particularly nice one a couple of years ago where I believe the tour guide was a member of the family who owned it, and they had a fantastic collection of old furniture, art, weapons etc. And the biggest holly tree I have ever seen (we're talking castle-wall height).
It's something we kinda take for granted in the UK. We have a lot of ruined castles that are obviously pretty empty, but if it's got a roof it probably has lots of old stuff to see inside too.
I do like the number of castles in France though; there's always something to see nearby. It's fun to be in a place with so many historic buildings, like here in Wales (~600 castles)!