In The Great Fairy Tale Tradition, Zipes includes siren stories I hadn't read before-Straparola's "Fortunio and the Siren" and Mailly's "Fortunio" are variations of basically the same plot (details below are from the Straparola)
John William Waterhouse
A couple adopts a child (Fortunio) and then has a child of their own. One day the natural son revealed to his brother that he was adopted, and Fortunio felt so grieved he left the house he grew up in to wander the world. But his adopted mother, who did not want him to leave, cursed him and prayed that if Fortunio should ever journey by sea, he would be swallowed up by sirens.
Fortunio travelled for a while and came across a wolf, an eagle, and an ant who were in disagreement about how to divide some meat among themselves, and they decided Fortunio would be a fair judge. He apportioned the meat wisely, according to what they could eat best, and the animals were grateful and rewarded him with the ability to transform himself into one of their kind at any time.
Fortunio continued his travels and happened upon a country in which the king had proclaimed that the winner of a certain tournament he was holding would win the hand of his lovely daughter in marriage, and on that day the winner had been a foul-faced and deformed man, and the thought of being married to him caused the princess much distress. That night, as the princess came to her window, Fortunio turned himself into an eagle and flew up to her, then revealed himself as a man. The princess shouted out at the presence of a man, but Fortunio changed forms as soon as anyone hurried to her rescue. Finally Fortunio was able to tell the princess of his love for her and his intention to win the tournament. He did so, and he and the princess were married.
After being happily married for some time, Fortunio decided it was time to go on a voyage, and he prepared a large ship and set out into the ocean. But next to the ship appeared a beautiful siren, singing softly. Fortunio leaned over the side of the ship and fell asleep, and the siren took him in her arms and plunged deep into the ocean with him.
Fortunio's wife and country were much dismayed at his disappearance, and his wife decided she would take their child and go in search of him, despite the dangers. She brought with her three apples-one of brass, one of silver, and one of the finest gold. When the siren saw the child playing with the bronze apple, she wanted it, but the queen told her she did not want to give away her child's plaything, so the siren promised to show the woman her husband up to his chest. The same episode was repeated with the silver apple, which brought Fortunio out of the water to his knees, and the golden apple brought her husband all the way out, and he transformed himself into an eagle and escaped, living happily with his wife and child.