You go to jail for failure to abide by a court order. Which is still distinct from going to jail for your speech.

Alex Jones can continue to say whatever he wants, from a criminal perspective. He may be somewhat more aware of the potential costs of being a professional liar now, which might cause him to make different decisions as he analyzes the cost/benefit ratio for something he wants to say.

The government won't stop him from saying whatever he chooses to say. The government might enforce costs, should he be sued for what he says and is found liable.