Tell me about Everest.
Everest is generally regarded as one of the best restaurants in Chicago. It is appropriately priced :) The atmosphere is relaxed formality. All the proper service is attended to, but it doesn't feel stuffy. It is 40 or so stories up, so the view (South and West, mostly) is very nice, especially at sunset. You'll want to dress up, but unless you are pretty scruffy, even business casual is probably do-able.
I'm not sure if I can characterize French Food as a whole in this space :) Everest is more Alsatian, as Jean Joho the chef is from Alsace. That is a region in France along the German border.
They have one of the best wine lists in the country, and if you want wine with dinner but don't know wine, they will help you find a good match. It helps if you know what you do and don't like (so if you know you don't like merlot and do like cabernet sauvignon, that's a good start)
I have actually eaten at Everest, and although I am generally unfamiliar with French cuisine, everything was exquisite. I particularly liked the lamb... At the time that I went, which was around 8PM, I felt that the atmosphere was pretty "casual yet formal". I didn't see anyone in business attire, but that doesn't mean anything. It is very subdued and classy, the view is wonderful.