Looks like the only flight into BNA with award availability on 2/14 is the early afternoon flight from ORD (UA3702). Unfortunately, it takes off at 1:15 PM, which is too early to make any connection from CDG.

As you already found, the early AM flight from IAD on 2/15 has availability, but that means an overnight layover. I am not sure if United will allow that on this itinerary, but could be worth a shot.

I would not book the 6:05 PM flight out of Midway.

There is a seat available on 2/13 if you can flex your travel by a day. Air Canada routing Paris to Toronto to Nashville....