What about "Hun fangede mig?"
That would work, too.
That is the correct translation. Hopefully someone will correct it soon.
Is this what "fik fat" means?
Is there a non-modal verb, or is this more common?
"Fik fat" literally means "Got a hold of".
"Han fik fat i bolden" = "He got/got hold of the ball".
"Politiet fangede tyven" = "The police caught the thief".
My Danish wife says that "på mig" should also work :)