The problem with a parquet floor is that the wood tends to run at 90 degree angles all across the pattern. In other words, some of the wood is going to be sanded at the 'proper angle' and some of it isn't. When you sand at the 'wrong' angle, you'll see the sanding marks.
Also, most types of parquet are held together by wire 'threads' and glue. This type of flooring may not stand up against a mechanical sander. Your first option is to have a professional floor refinisher access the floor for these issues. From there, you can ask your questions about still wanting to refinish the floor, or possibly replacing the floor, or doing nothing.