They can take the form of "sous-entendus" where the same sentence can be interpreted differently depending on the level of knowledge of the listeners for a particular context.
Play-on-words are also widespread, including the "contrepèterie" art form unique to French.
Various form of "argot" (slang) also use identical words bearing different meanings.
All of these are a big part of our second and third degree humour that elude so many foreigners.
This journalist from the BBC does not seem to be much aware of French culture at all.