It’s an old derogatory word similar to “peasant”.

In modern French, péquenot (redneck) might be used with a similar meaning.

In this song, croquants is definitely used to name peasants, and in this case relatively healthy and avaricious ones, as shows this verse:

Les croquants vont en ville, à cheval sur leurs sous

See the TLFi

Although croquant has a very definite meaning, Brassens is using the the metaphor with a rhetorical strategy to designate middle class persons, typically with reference to its perceived materialistic values or conventional attitudes.