I'm a US citizen living full time in France and have already exchanged my US driver's license for a French / EU one. As part of the process I had to turn in my US driver's license, which I guess they destroyed.
Now I'm back in the US, visiting (I maintain a US address at a relative's house) and actually have mail that my US license is up for renewal. In practice, I don't think there's anything stopping me from going to the DMV and getting a new one.
But I wonder if it's actually legal for me to have two licenses from two different countries simultaneously. In France I'm guessing it might not be, since they required me to forfeit my old license. And in the US I'm not sure. Having trouble finding the legal specifics of that.