Is "close helmet" correct? Why/why not?

Solution 1:

Actually, according to this Wikipedia article it is close as in "close the door."

The close helmet, also called the close helm was a military helmet worn by knights and other men-at-arms in the Late Medieval and Renaissance eras. It was also used by some heavily armoured, pistol-armed, cuirassiers into the mid 17th century. It was a fully enclosing helmet with a pivoting visor and integral bevor.

Also, being a technical and historical term, it simply is; even though it sounds strange and unfamiliar to our modern ear.

Several senses of the word as listed here are readily identifiable as sources for the usage.

Solution 2:

If "close" is a specific technical term for a type of helmet then "close helmet" would be just as correct as "Steel helmet" or "Norman helmet"

Solution 3:

Close is sometimes used as a modifier instead of closed; a well-known example is close-minded.