Please show us color - have no idea what paint brand has those colors, and also show us a picture of what you are calling "french style". That could mean anything...

I'd look for a tinted white/ barely there gray, as I prefer a white/neutral kitchen. as in this entry space gray door and light walls. You need to know the tones of gray cabinet paint- cool or warm.. Take a cabinet door to BM or Sherwin Williams or other paint store.....Ask staff to match it to one of their colors. Research palettes with that color. SW has several books that have pre-coordinated palettes --nearly all have a few gray shades.... Or web search example below. My current project: Laundry/ utility room was decided on colors we liked SWSea Salt and Eider White. The cabinet color is SWMindful Gray after reviewing many paint swatches. Then, last night I came across this, which reinforced the selections ETA. I hated the BM and SW color visualizers, those programs were not helpful. Search kitchens with gray cabinets. If a page doesn't have wall paint details, then save the image and use a Reverse Image search, which will show you to other sites with that image, like Instagram. It takes a bit of effort, but it is well worth it . Try: https://www.reverseimagesearch.com 

If we do end up buying, it will be a few years before we could do a reno. By that time, I probably won't even notice it LOL. But I think for the time being a colorful rug, towels, and such would absolutely do it favors! Maybe even incorporate a gray/brown color scheme into the family room could help the gray feel a little warmer. As far as the flooring, given time we could change out the tile along with new cabinets, appliances, and floor plan for the kitchen.

Then go darker - Dovetail is on the same color range. Or go white? But really just shooting fish in a barrel here - best to show us floor finish and exact countertop to best pick.