Can't see anything in that photo except that tile, which looks like real stone that I wouldn't replace. But perhaps better lighting would clarify what you're seeing...

Can you take a photo from the door or get some lights in there so we can see better? The floor looks really nice and if it's original I would clean it up and keep it if it is in usable shape. As apple_pie_order said, if the glaze is gone, they will be hard to use. I don't know if they can be reglazed?

As for the entryway itself, that chandelier looks very cool. I'd keep that. You could put a large round table underneath it or a bench/table and large mirror on the wall where that furniture is. A coat rack on one side of the door and a holder for umbrellas on the other.

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Take the picture with your back to the door. All we see is black white and grey because your camera lens is focused on the hedge outside.

I would not take up the stone. It can be restored with elbow grease and the right materials.

Thank you - I'm going to keep it and get it professionally cleaned. I'm also going to paint the walls a very pale grey with white trim which I think will make the tiles blaze again.

Not only professionally cleaned, but those old tiles can probably be professionallly polished and re-sealed.

Gnu36, I will definitely look into that! Thank you for the suggestion.

Are the tiles stone or ceramic?

Don't touch the tile! Precious....Refinish and use matching color tiles or rugs (blue and white?) to extend through to patch worn areas. Lucky you to have an authentic French farmhouse! Bonne chance!