If you don't have a separate document that is solely RFC, you don't have a copy of your RFC document--you only have a document that shows your RFC number. A Constancia sits "on top" of your CURP and RFC and verifies that SAT confirmed the legitimacy of both document numbers assigned to you, so a Constancia shows your CURP, RFC, and registration ID number in the SAT system to the right of the box and next to your QR code.
Did the papelería have you go through the visual, signature, and oral-reading prompts? Did they give you your own login and password to reprint your Constancia when you will need to? The Constancia (as do many Mexican documents, including birth certificates) have an expiry date of 30 days from the issue date printed on them (see the box under the document title CONSTANCIA DE SITUACION FISCAL). To reprint, you have to be able to log in to your very own account on SAT with your user ID and password, which you select during the preregistration step. (The process for a Constancia is twofold: pre-application and approval by SAT after review, then setup of your SAT account and printing of your Constancia. Sometimes this takes a day or two.) If you don't have the aforementioned information to get into your account and to reprint, you're likely going to have to do the process over when your Constancia expires, as have several people I know who chose this workaround route, rather than fully complete the process through SAT.