North Carolina voters approved a voter ID amendment to the state constitution; I assume that carries more weight than the voter ID laws that have already been overturned, but can the federal court still take action?
Yes. The Supremacy Clause of the U.S. Constitution overrides any state law -- even a state constitutional amendment.
Article 6, Paragraph 2 states:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
The only thing that a state constitutional amendment accomplishes in the case of North Carolina is that it prohibits judges within the state from overruling it -- even on constitutional grounds (since an amendment is part of the constitution, you can't rule it to be unconstitutional).
A Federal judge can still rule NC's amendment unconstitutional per the federal constitution's supremacy clause, but it must be a Federal judge that does it.
The comments this answer has generated indicate that I need to clarify my last statement. I was speaking of NC's voter ID amendment specifically.
It needs to be said that there is no federal law, nor any federal court precedent that forbids voter ID laws in general. In fact, 17 states already have them. Therefore, NC's amendment does not violate the Supremacy Clause by itself. NC's voter ID amendment only states that a photo ID is necessary to vote in person at a polling station. That's it. Nothing more.
The purpose of the amendment is that it requires the state legislature to pass laws specifying the details of what types of ID are acceptable, what ways a person may go about getting one, etc.
State judges may rule that certain provisions of laws passed by the legislature are unconstitutional federally, or might violate the Supremacy Clause due to federal law or precedent. But no judge on any state bench can rule the amendment itself to be unconstitutional. Basically, North Carolina can't not have some kind of photo ID requirement because of this amendment, and no state judge can change that.
Only a federal judge, or an act of Congress dealing with the merits of voter ID as a concept can invalidate the amendment.