While talking with my friend I told about one person
that he is a half- frantic man…my friend who has good knowledge in English,
he argued that there is no usage like half-frantic.I learnt somewhere half-frantic almost equivalent to half-mad
is this correct? even I tried Google search but couldn’t find such a word.is this old usage??

“half-frantic” is fine in the right context. It means in an agitated state, somewhere short of being truly frantic (though in practice there sometimes may not be a huge difference between “frantic” and “half-frantic”). I don’t know why you couldn’t find any examples through Google; I can see hundreds ( google.co.uk/search?q=%22half-frantic%22 ).

The term normally describes a temporary state rather than someone’s overall character. To say someone “is a half-frantic man” seems to be describing the man’s overall character, in which case it would be less usual, though not impossible.