Jean-Pierre Jeunet got the idea for a cannibal butcher when living in an apartment above a butcher's shop. Each morning at 7am he would hear the metallic clash of knives and a voice shout, "Chop chop!" His girlfriend said he was carving up the neighbors, and it would be their turn next week.
Delicatessen was the first full film made by Caro and Jeunet, but it was actually planned after The City of Lost Children (1995) was refused, because "The City" was too expensive for the, at the time, unknown directors to assume. For that reason, Delicatessen's budget was cut VERY tight, with a very restricted set, many friends and family of both directors appearing in the cast, and most props being actually old scavenged stuff - again, to cut costs.
Many elements of cause/consequence make the film ever more interesting to watch again and again. One such example is a couple always using the same prophylactic (a condom), of which the husband (Ticky Olgado) takes great care: it has been patched twice. Hence, the couple has two kids.
Jean-Pierre Jeunet got the idea for the movie in 1988 while vacationing in America. He said after staying in America's hotels he felt the food was so bad that "it tasted like real humans". Then came the idea.