I do suggest you try cleaning it as paint will wear out - especially in a foyer where soil from the outside can really do a number on floor paint unless you have lots of walk-off matting.
I'd try cleaning with Jon-Stone Liquid Poultice from JohnsonDiversey. Follow the instructions on the label - you'll need a wet vac & possibly a deck brush. When it's done working suck it up with the wet vac, flood the floor with water, since & suck again. Repeat if needed. If this doesn't work then I'd try painting. If it does I'd seal it with a good penetrating sealer like JohnsonDiversey's.