The Moulin Rouge is probably the best known of the venues in the bohemian Montmatre district of Paris in the 1880s, but it was primarily a music hall, and it was only one of the variety of entertainment establishments.
It is recognised that Le Chat Noir ('The Black Cat') is probably one of the first established cabaret venues (One of its specialities was Shadow Puppet shows!). Other Cabarets included 'Ciel'(Heaven) and 'Enfer' (Hell), located next to each other, with doormen and waiters suitable attired as Devils or Angels, and themed food and drink.
These are early examples of theme restaurants, although some might say others took things a bit far: Wikipedia (and 1897 books on Montmartre, by Renault and Château ) tell of Cabaret du Néant, "where a sinister irony was expressed, not with angels and devils, but with people, mortals, death". M. Dorville was the founder and owner of this cabaret of Death where, by aid of mirrors, the customer is made to witness the decomposition of bodies, where the tables are coffins, the diners are the dead, the waiters are the undertakers, and so on and so forth".

Other themed venues of the time included Le Divin Japonaise, a Japanese themed concert bar, which still exists in a broader format: Fantaisies Parisiennes, which became a theatre dance bar, and Le Cabaret des Incohérents / Café des Décadents. More about these clubs can be found in the article 'Beyond the Moulin Rouge' (https://jetaimemeneither.com/historic-cabarets-of-montmartre-paris/)
Clubs for which Paris is now known such as the Follies Bergere grew from these beginnings.