The market is called "Miyazu Eemon-ichi(宮津ええもん市)". Food stalls are available. This market is good for if you are interested to discover local food :) Some popular products are sold out within 30mins after the opening.
Location: Miyazu City Gym(Miyazu-shimin-taiikukan宮津市民体育館)
From Miyazu station walk about 10mins.
From Amanohashidate station, take a bus toward Kamimiyazu(上宮津) and get off at Kisenba-minato-kan(キセンバ港館) and walk about 1min. Bus fare(single) 200JPY/person.