The type of floor is one part of the problem. Lots of floors are slippery, and that causes fear in a dog. The other part of the problem is the length of the dog’s nails. When his nails are too long, he is walking on “spikes” instead of using the natural grip of the pads on the bottoms of his paws.
A dog that is inside or on a lawn all the time misses out on the natural filing of these nails on dirt, rocks, concrete, etc. Getting his nails trimmed is a good start, and so is putting down one or more throw rugs with a good rubber backing to prevent them from sliding.
After you have done both, gently but firmly lead your dog in the room or building and watch his anxiety start to melt away.