Please help me with building a paper tape reader (punched tape)

What is this tape from/for? You mention CNC - is it a CNC program tape? Do you know what machine it was for? Do you have the manual or other information for that original machine? Do you have scan or a picture of the first foot or so of holes on the tape?

Your first goal should be in identifying this information if possible; if it is an old CNC program tape, talking to some old-timers who used/programmed such machines might be helpful (if you can locate one). Otherwise, you might find something regarding the coding online, or in a book (I might have some information in my personal library, if I knew more about the tape).

Without seeing the tape, the 9th hole could be a parity-check hole, it could be a timing hole, or it could be an indexing hole for an advancing cog (or a combination of the last two); it could be that the data is encoded in 7 bit ASCII with the 8th bit being parity. It might be in EBCDIC or Baudot code for all anyone knows.

Once you know the encoding, then you can think about decoding it. Building something with an Arduino is possible, but it might be simpler to scan it and decode it that way, as already mentioned (heck - have you looked to see if maybe somebody has already done all the hard work of this?). Either way, before thinking about the hardware, you need to get a grasp of what the information on the tape in encoded in first if you can.