David
I take this route quite often it is easy to get boarded even if the flights are overbooked there are a lot no show.
If you can get a ZED ticket on AA it is a possible back up however their flights tend to be full.
I do not know if TN still fly this route.
Of course there is also DL but if it is an ID90 it will be costly due to the YQ added.
If you are on the west coast remember that AF fly SEA/CDG, and of course they have some flights from LAX as well as TN.
Good luck.