Was Robert goulet gay

No he had 2 wives

This is not proof that someone is or is not gay. Many people marry for "cover", celebrities especially, quite often.

Edit:

Kevin McCarthy a popular talk radio host in Dallas in the 1990s relates that one time after an interview Robert Goulet leaned over to him and said "You know Kevin, you are a VERY handsome man" or something to that effect. Kevin continued to get their famous Christmas cards for years after.