A similarly themed restaurant could be found at Magic Kingdom, under the name Cheshire Cafe.
Disneyland Paris version
It located close to Alice's Curious Labyrinth, guests can have drinks near the Hare's house. Like in Walt Disney World and in Tokyo Disneyland, the Dormouse can be seen popping his head out of a large teapot and the March Hare, although absent, can be seen on the sign of the doorway.
Mad Hatter's Tea Cups is located close to this house as well. Back in April 1992 when the park opened, March Hare Refreshments sold Unbirthday Cakes (Gâteau de non-anniversaire) for 19,00 FF each.
Magic Kingdom version
When Walt Disney World opened in 1971, the area where Cheshire Cafe and its adjoining restrooms now sit was actually part of Tomorrowland. Around the same time, Disneyland had created a section inside Fantasyland which focused on artists creating souvenirs for guests featuring their name in creative lettering or silhouettes of the guests (that section is still in Disneyland to this day). Due to this popularity, Disney created the Fantasyland Art Festival.
The Fantasyland Art Festival remained open until the early 1980s when it was transformed into a quick service location as The Enchanted Grove. The Enchanted Grove offered guests the opportunity to grab quick snacks that could be eaten on the go. The area remained practically untouched up until 2011 when the snack location was rethemed to help fill in the overlaying storyline of the New Fantasyland project by focusing more of the area around the Alice in Wonderland story.