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Phrases and Idioms
F
A type of bazaar where inexpensive goods are sold or bartered.
Flea markets have a wide variety of items available for interested customers,
e.g. fresh foods, worn clothes, furniture, and much more. People go there to
exchange goods, either by buying, selling, or bartering for an item.

Often times, flea markets will be located outdoors, either in large fields or under big tents. Since they take place outside, there's a possiblity for insects (like fleas) to get on the items being sold or bought, and even the people attending. On that note, according to Wikipedia, one of the theories as to where this phrase originates from is the French 'marché aux puces', which literally translates to 'market where one acquires fleas.'

One of the oldest and most popular flea markets is located in Paris, France, and it has held the name Les Marché aux Puces (the flea market) since around the 1870s.
Common Phrase Origins and Meanings > F-Letter Expressions
For most of the common expressions, sayings, and idioms, finding where they originated exactly is nearly impossible. Normally what's provided is around the oldest time a phrase was recorded in a book, poem, or play. Sometimes, there will be an early printed use of a phrase in an old newspaper, which will often be quoted to give you an approximate age for the saying.

However, it should be noted that if a certain idiom is being used in a form of media, like a newspaper, then it's probably already a commonly known saying, thus, it should be assumed that the phrase origins are probably from an older time.
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* We're going to the flea market later on today to see what we can find, you can come with us if you'd like."

* A flea market is supposed to be coming to our city in a few days, so I'm going to stop by and see what they have for sell and maybe trade away some of the junk we have taking up space in our garage.
Flea Market phrase meaning.
Origins for the idiom Flea Market.