Restaurants exist recreating food and dining expericances from the middle ages (Medieval Times, are there any that try to recreat an ancient Roman dinner party? Or serve ancient Greek cuisine?
I went to a couple in Scandanavia that had Hanseastic League-era cuisine. It was really good.
There used to be a resaurant in Anchorage that specialized in Tudor-era food and the whole dining experience ala Medieval Times. Turkey legs, buxom wenches and all.
This place kinda tried
And if you ever find yourself in Trier, Germany you might be in luck.
Judging by the quality, some of the food that our works canteen serves was pretty ancient before it went into the pot. 
Not what you are asking for but you may be interested in the TV documentary Three Emperor’s Dinner if you can find it. An Aussie chef attempts to authentically recreate a famous meal from 1867.
Turkey legs and buxom wenches are hardly Tudor-era food or ambience.
If I ran a restaurant, it would serve High Medieval - Early Renn food in a proper Medieval setting (so no wenches & benches). Everything from Chaucerian Blancmange (a chicken&rice dish) to waffles for dessert. Once a month I’ll do a quail-in-a-hen-in-a-duck-in-a-goose-in-a-pig roast. Turducken, eat your heart out…
The Bors Hede Inne is an attempt to provide reasonably authentic medieval food to a general audience. In practice, it comes out a little meh, but you gotta give 'em points for trying.
“So I order french toast during the Renaissance.”
If you’re ever in Cordoba, Spain, check out El Caballo Rojo. I have no way to verify its authenticity in terms of faithfulness to ancient ingredients and modes of preparation, but the stuff on the menu is certainly different than what I’ve ever had in any other Spanish restaurant, and is in agreement with what little I know of Moorish cuisine.