The real nexus of programming and mechanical engineering is embedded software. Microcontrollers have become powerful enough that Python and JavaScript can be used where margins are fat and bean counting is balanced against programmer productivity. Of course, tradition and commodification of hardware make other languages more common.
Then again, learning more languages is probably going to be part and parcel of a programming career for any recent grad.
Good luck.
The C++ software engineers are all from traditional engineering backgrounds (cannot remember their degrees though, sorry), as you do need the more "advanced" Calculus to understand our stuff. I think this is where you should be looking at - simulation/engineering software companies - if you have the chops.
Good luck!