Why not just use the simple term "text box"? That seems to be the most appropriate term and is quite likely to be understood by everyone.
I don't think "free-form" is a commonly used term. On its own, it sounds strange to me:
Please enter your comment in the free-form below.
You can also use "text field", which sounds more natural than "free-form", at least to me. But what is natural really? Who is your audience?
"Free-form text box" or "free-form text field" would be fine, but they just add more words that are not necessary to say what you are referring to.