OP - Are you on one or two tickets? AF & UA most certainly do interline bags. But, neither will interline across tickets.
If on one ticket, you may possibly have a fighting chance. If the latter, forget it.
Rather than changing your UA flight, what about simply purchasing a new AF ticket for the night before and spending the night at a CDG-area hotel? A heck of a lot less than $5K. AF tickets at roughly $175.
UA might or it might not let you stand by for its next flight, but it won't commit to that in advance until you actually now show. Maybe you get onto its next flight and, depending on the rules of your ticket, you have to buy a new ticket.