Looks like I got here too late!!
From the picture it looks to me like limestone or travetine. Either way it does not look man made, and if you can't tell then don't mess with it!! If there is a repeating pattern, it is man made. If every tile has a different pattern or vein structure, is is natural. Natural stone must be honed and polished to get a shine. Do not use a bunch of crap on this floor and end up destroying what is left of it! Ceramic tile needs no finish on it, it is what it is. Step aside, and tell your client to call a professional tile cleaner/restorer to fix this floor before you end up buying it!!