The President nor his cabinet can negotiate any treaties with anyone without Congress. If the people's elected representatives were not at least present, it's cut'n'dry.
This is exactly what they hanged Benedict Arnold for, similar circumstances and the same theme. It was a no-brainer back then, it doesn't take a rocket scientist to figure out what charge is appropriate now.
Conspiring to betray the constitutional borders of the country to foreign agents is such vile duplicity I don't think it warrants a jury trial. Any lamp post would serve.