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Unfortunately, there is no means to find out if the user had already printed or not the form on their end. The PRINT button have no such functionality to capture action if it had been used or not by the user.
But a workaround you can do to force the user to always PRINT FIRST before submitting, is like this.
Again I want to emphasize that my idea is not fool proof -- the user can still find ways to submit without printing if they really seek to do so.
You can do so by adding a another submit button on the form. And use Condition Logic to make the Submit button only available if the user have filled in the form questions and had it printed.
This guide will be use https://www.jotform.com/help/57-Smart-Forms-Using-Conditional-Logic
Here is a demo form http://form.jotform.me/form/41137387520452? you can try where I have used the suggested workaround.
Please inform us if you like the idea so we can apply it on your form.