A new Parisian startup is selling merch — a word “you can’t even translate into French” — for some old-school establishments.

Whirling 360-degree photo booths have gone from red carpets to bat mitzvahs to tourist sites like the Cradle of Humankind.

Buon Ricordo plates were introduced 60 years ago at restaurants in Italy. The hand-painted ceramics can now be found at design trade shows and fancy...