The floor covering was taken out and left as a concrete floor. Now the toilet has space between the bottom and the concrete. Can I shim this in some way or do I have to reset the toilet?

You can use toilet shims and caulk but a better way is to cut the old closet flange and install a new one. How big is the gap?

I agree with ma064 about removing and lowering the flange. What material is the flange and pie? Back to you, Tom