1. As far as terminology, he wasn’t gay. He had gay sex. Gay/homosexual weren’t terms used to describe people, they described acts. Everyone was presumed straight.
2. As the King’s brother and a Duke, his position allowed for him to do pretty much whatever he wanted. Had he been of low birth, things would’ve been different.
3. He was raised as a “girl”. I quoted it because he wasn’t literally presented as such, but he did grow up wearing female clothing and doing more feminine things; he was discouraged from war and other man stuff. This was to keep him from overshadowing his brother, the King. Louis 14 became King at age 4 and his mother was Anne of Austria, a Spanish Queen, was Regent. Spain and France were in kind of a constant turmoil for a lot of the 17th century, and she had also been accused of cheating (people were suspicious when after over 10 years of marriage she finally managed to produce an heir). Louis 14 needed to be the unquestionable King.

In short, he wasn’t openly gay. He did gay things and dressed like a woman, but he was officially a straight man.