What is the verb for "apoplexy"?

Solution 1:

An apoplexy is typically not a long-standing medical concern so you don't really "get or "contract" apoplexy.

In your example I would go with:

He experienced an apoplexy...

or

He suffered an apoplexy...

Also, due to the ambiguity of apoplexy as a condition, medical staff generally refer to the part of the body concerned, as in "a pituitary apoplexy" for example.

Solution 2:

Try:

He was struck by apoplexy [...]