What kind of stone floor? Sandstone, or a carbonate like limestone or marble? If an old country house, may be a local stone.
I re-did a stone table-top that had wine stains (and etc.). I used a fine grit to take down the surface. Then re-polished with an even finer grit. It was an irreplaceable antique pink marble that can't be replaced.
Carbonate stone is easy to grind down and re-polish but hard sandstone, granite, etc. is difficult for an amateur without proper tools.

Digression-
I have a marble entry. I found enough c. 12x12 marble slabs at a place which had leftover material, as cheap as top-quality vinyl. I bought a few extras just in case someone dropped an anvil, acid substance, or whatever.
Our kitchen is ceramic-tiled, replacement for old vinyl, but we bought extra when that was put in.
Both would undergo repolish as well as replacement, however.)