To answer the title question first, yes, it is. Roughly, I am going to say that it happens incidentally 90% of the time and intentionally the rest of the time.
This comes from innocent ignorance 80-90% of the time as the English word "flea" is simply not known nearly as widely as the word "free" among the average people. The word 「フリー」(from "free") is already very common and most of us just never questioned our notion "フリー = free".
There is the old term that everyone knows 「[蚤]{のみ}の[市]{いち}」, which literally means "flea market" but we just fail to make the connection between 「蚤」 and "flea". 「蚤の市」, by the way, is the translation of its original French term "le marché aux puces". It does not come from "flea market" in English in case that is what you thought.
So, it was coincidental in the vast majority of cases. However, there are times when people who are actually familiar with the English term "flea market" use on purpose "free market" as the "spelling" for THEIR own flea markets. This is where what OP states in his paragraph #2 comes in. I have personally seen advertisement where "Free Market" is used in its English spelling with an explanation saying that freedom is the key word. You can sell anything for whatever prices you want. You can even choose to barter instead of sell. You are free to do anything!
Finally, a word on the tricky term 「自由市場」. It has not been explained fully as I type.
When read 「じゆうしじょう」, it means "the free market (system)" as an economics term.
When read 「じゆういちば」, it is (part of) a proper noun for a "flea market" type of an event or place that someone is running.