Well, I think you have partly answered the question. Many people either do not know that the family is called that of the Romance languages (they think it is called "Romantic") or know the name but don't make the link to Latin but to love.
I don't consider Spanish to be any more romantic than any other language. I am aware that there are some strange stereotypes about how French is the language of love (light would be more historically accurate), how you can't speak Italian without a smile (?!?) and how Spanish transmits joy. These are all based on cliches about the supposed passion and joie de vivre of these cultures. Some of these cliches have an ugly root in a form of racism that suggests that people from these regions are "hot-blooded" and impulsive.
People who are superficially interested in culture as something exotic that serves as a form of escapism repeat the same cliches and reinforce the stereotype, though it isn't true. It is perfectly possible and common to speak Italian while glowering at someone or looking dour. French-speaking guys are not any more romantic than Russian-speaking or English-speaking ones. For every joyful and carefree Spanish speaker, I bet you can find a serious, anxious and melancholic one. It is all highly individual.