Mirrored french doors? Chocolate brown walls will look stunning with both the wite doors and with your wood staircase.

As far as the staircase. I am painting a staircase in my home right now that looks exactly like yours with the exception of having two landings. From what I can see your stairs may have one landings. Doesn't matter but we are painting the handrail and the spindles in a semi-gloss white. The risers ( face of the stairs) we also painted in white.

It took me many hours to tape off the just spindles under the hand rail because initially I was planing to either re stain the handrail back to its original color or paint it Black. I Used the best painters tape I could find on the market.

After painting the spindles and taking the tape off I still could see white paint here and there on the underside of the handrail. You could see it especially if you were looking up the stairs from the bottom of the foyer. I decided to go ahead and just paint the hand rail white as well. To my surprise the handrail all white with the spindles white and the faces of the stairs white looked gorgeous! It updated my foyer and brought so much more light to the foyer. I do plan to buy a Dash and Albert runner ( going all coastal in my home)to go up the stairs to also refresh the foyer. You can do that as well with a fun runner you may like

May I suggest a large chandelier that would brighten up your foyer? From the pictures it appears a bit dark.

The wall paint revere pewter could look lovely against an all white stair case. You have a lot of wood trim on the back wall. You can either paint that all white ( as it seems to be part of your stair case ) or you can paint the walls and the inside of the panels on that wall revere pewter( or whatever paint you choose for the walls) and the outside of the panels all white. Just to two tone them a bit and blend them with the walls.

The closet doors will look completely different once you update your staircase and you can always change the knobs to get a different look. Hope this doesn't come too late