Wordorigins.org

Generally, the word flea connotes low-rent or cheap, because such places were often infested with fleas (cf. fleabag). The term flea market is a translation of the French marché aux puces, literally market with fleas, an open-air market where second hand goods are sold. From George S. Dougherty’s 1922 In Europe:

It is called the “Flea” Market because there are so many second hand articles sold of all kinds that they are believed to gather fleas.

Some suggest that the term is also influenced by the fact that the locations of such markets are not fixed and jump around like fleas. While this may be a characteristic of the markets, it does not appear to be the origin.

(Source: Oxford English Dictionary, 2nd Edition)