Few carriers any longer will willingly ticket a ticket which does not at least involve a segment they operate, typically the first segment. That is why MEX-CDG on AM does not show up on DL. DL has the ability to ticket this and you should try calling DL to arrange this. It may take some doing and a few calls, but it should be possible.
Very unlikely that Mexico immigration or customs worries particularly about your routing. If you are asked, simply tell the truth. Many people schedule international positioning flights to save money so it is odd and easily explained if questioned. As always, it makes sense to print out hard copies of your e-ticket receipts showing your outbound ticketing arrangements. (You may also need those at BNA before DL boards you).
Your risk here is, of course, that you are not connecting and therefore connections times are irrelevant. If your BNA-MEX flight is cancelled and delayed, you are completely at AM's mercy and your AM ticket may be reissued for a later flight or you may be required to purchase a new ticket at walk up prices, all depending on the fare rules for your ticket and whether you happen to run into a sympathetic agent. For this reason I would suggest booking an overnight at AM or at the very least 4-6 hours at MEX in order to account for routine delays.
Reservations cannot be "linked". All DL does is make an entry in the PNR notes with the AM e-ticket number. That won't matter on this travel.