If it is James Farmer's market, then it is Farmer's Market.
If it owned by a group of farmers, then it's Farmers' Market
If it is a market place for farmers to sell their product, than it is Farmers Market.
Just my way of understanding it.
That's very close to what I think about all this. #1 is indisputable - when the owner is one person it's his market, say, Adam John's market or Terry Karmichael's market. However, much more often we have the case when a market is intended for farmers, who come there to sell milk, cream, sour cream, curds, butter, vegetables, etc. I would suggest either
"farmer market" without the "s" or the apostrophe. "
FarmerS market" is also OK. The diference between the two, as I perceive it, is that a "farmer market" is the place where farmers doing similar things collect. For example, farmers selling only milk products or farmers that have all come from one place. In other words they have all something in common, which allows us to attribute them to one category of farmers. This feature can be their produce, the place where they've come from, their age, etc. "FarmerS market" tells me that there are different farmers and they either sell different goods or are distinguished by some feature. Finally "
farmers' market" with the apostrophe can mean that several farmers own it, but cannot it mean the same as "farmer market" or "farmers' market"? Does the apostrophe always have to mean that they (farmers) own the market?