No agreement here - other than you won't find fleas for sale if you go to one. There are two (vaguely) plausible theories:
1. A translation of the March Aux Puces - often used to describe a large outdoor market in Paris that became popular in the 1920s "because there are so many second-hand articles sold of all kinds that they are believed to gather fleas." [E.S. Dougherty, "In Europe," 1922].
2. From the Dutch word for swamp is given as “vlie”, which sounds like flea when spoken in English. The Dutch settlers held markets in the then swampland that was Manhattan Island.
The OED goes with the French market explanation which, while less cute, is more convincing.