Kelsey:" I think I now comprehend the idea of circling, but I'm not sure how he is supposed to say what he has when he doesn't have the words for "horse" or "bike" yet. Should he say it in French, then I write it on the "board"? (I think I'm just going to have a piece of paper between us to act as the board) for him to refer to? Or should I not make him talk at all?"
It's okay for him to say "cheval" which shows that he's understood your question. And yes, write it down with the translation. Horse = cheval. Then say it. In TPRS classrooms very short, one or two word answers in the first language are allowed when students don’t have the vocabulary they need. So they are not kept from participating and you can decide whether it’s a word you want to teach or not. If you think it useful, you translate the word, put it on the board (or a piece of paper) and refer back to the written translation as often as needed. This is called "Point and Pause." You point at the word they need and pause to give time for processing. What you don't want is a long complicated answer, often with a subordinate clause :-(, because you don't want to get side-tracked.
And you'll find that there are a lot of English expressions that have been adopted into French. We call them “transparent”. (When I use the film "Shawshank Redemption", there's the word "turnout" which I always had a lot of difficulty in explaining to my students. Then I went to a student's house and she asked where I had parked. When I explained, she said, "Oh, vous vous êtes garé dans le turnout." She's from the north of France, and it seems that they call the turnout "un turnout".
Remember, when you start in on your story, you can accept or refuse his suggestions. It’s always your story. So, unless he's very interested in horses, I'd prefer bike, because it's used more often. Keep your vocabulary as high frequency as possible. If he brings in a French word that you hadn't anticipated, think about how useful it will be before you decide whether or not to go with it.