Question: So we call a French male "Frenchman", an English male "Englishman", and a Dutch male "Dutchman". what do we call Swiss males?

"Swissman" comes to mind, but it sounds like a cheesy version of Superman, like "Cheddarman" or "Mozzarellaman".

Answer: 
There are in fact [very few cases](https://english.stackexchange.com/questions/113774/why-do-only-a-few-english-demonyms-indicate-gender) where the customary demonym is *root + -man*— those you have named plus *Irishman*, *Norseman*, *Welshman*, *Scotsman*, and (obsolete, now considered offensive) *Chinaman*, and maybe a few others in Britain like *Yorkshireman* or *Cornishman*.

In the absence of a more established form, the [demonym](https://en.wikipedia.org/wiki/Demonym) is usually the same as the adjectival form. Just as we would speak of an Indonesian, an Omani, or a New Zealander, we would speak of a **Swiss**.

It sounds abrupt, even to this native speaker, not only because it is monosyllabic (e.g. calling someone *a Japanese* also seems off), but because in today's politically correct age, referring to someone solely by their nationality or ethnicity is potentially problematic. It would be preferable to use the demonymic adjective in conjunction with a noun; *Swiss man* would suffice.
Whichever the nationality, it is an Adjective in a Noun Phrase, whether you tag on a denominator or gender or other such noun. 

So, "I'm a Swiss (man / woman / citizen / denizen / etc.)" is fine. Or then simply say, "I'm Swiss" leaving out the [indefinite] article. 

(Please do post a comment if you don't agree with me).