Edward III has a very mixed up parentage. His father is Edward II and his mother is Queen Isabella of France. But in 1995, the film Braveheart (which i did not like one little bit), portrays William Wallace as Edward III's father. This theory must be destroyed and I attend to do it.
First, in the year 1298 (which is not the year Wallace died; he was killed in 1305. Edward I wasn't sick on that day, but out hunting.) Isabella was a six year old girl, living in her fathers kingdom of France. Her marriage to Prince Edward wouldn't be discussed till the next year and she wouldn't come to England or marry her suitor until 1308, at the age of sixteen. Edward III wasn't born until four years later. So in no way could William Wallace be the father of Edward III. It's a good fiction, but a fiction nonetheless.
But there are other theories. One, given to me by my cousin last year was that Edward III and his siblings were a result of an affair between their mother and an unknown Frenchman. This is more plausible. Edward II was not a very good husband, and didn't pay much attention to his wife. He was to be found more often in the company of his favorites, like Piers Gaveston. He was even rumored to be bisexual. It is easy to see why Isabella might have thrown herself into the arms of a handsome Frenchman. The problem is she didn't. She was a loyal wife and did not get involved with Roger Mortimer, her known lover, until 1323, two years after her last child, Joan was born.
In this explanation we can be sure of two things. First, Edward, John, Eleanor, and Joan were all fathered by Edward II. He may have not doted on his wife, but he did sleep with her. The second thing is that all these stories were fictions; one in a movie, another in a negative chronicle. Edward III was not illegitimate. There is no 'if' in that answer.