I love this picture! What a nice-looking bunch of people! Unfortunately it doesn't show the floor in question LOL

I would not recommend gray with the terracotta floors. Pick a warm white and a nice quartz in white with grey veining, something like the first picture.
I love the hardwood counter on the island in the second picture (not sure if you have an island or not) Just do a search on 'terra cotta floor in kitchen' on Houzz and you'll see a gazillion ideas!

I have terracotta floors that pull pink. For a dark grey, try BM kendall charcoal, for a lighter shade try BM white dove. For a warm white, Dunn Edwards Shortbread or SW Dover white also look good with the tile.