Under these treaties it doesn't matter if a law is based on the constitution or not. If the trade courts rule that a country's law violates the treaty the country will be punished via trade protectionisms such as quotas or import taxes.
Thus far, no actual treaty has ever been invalidated; the closest is an executive agreement in Reid v. Covert: https://en.wikipedia.org/wiki/Reid_v._Covert
In other words, we can't force other countries to not all agree to raise tariffs on goods that they import from the US. The constitution doesn't matter, because they are foreign governments. Our laws have no bearing there.
If that wasn't the case then any country could use their laws to force people in other countries to do whatever. Certain activities would be both required and banned at the same time. Here in the US it's illegal to coerce a voter, and in Australia voting is mandatory. There's no way to reconcile those two laws.