You need to do more research. His second wife never had children because she was herself a child when he died (marrying kids was a common political practice back then), and back then gay royals DID usually have children (France's gayest prince, Duke Philippe dâ€™OrlĂ©ans,Â managed to produce three).
Lack of children does not automatically mean gay, especially in the noble classes back then. Gay royalty were expected to lie back, think of England and produce a bunch of heirs.
Was he gay? Possibly, but your arguments are fatally flawed in several areas.