Un animal de bât is indeed a pack saddle animal, and bâtard is indeed a bastard so that's pretty cool. Never realised the connection! -ard in French is also often a negative suffix, like connard which would be a... "cuntard" if you will.
-asse is the feminine variant, although there are inconsistencies, such as pétard / pétasse which are probably related but one is a firecracker, while the other is a tart (the lady kind)

Rude language is always so much fun!