N_Samijo:
I understand your concern. Tax preparation
can be rather confusing.
Your co-workers are correct. The $5,000 tax exemption applies to the state income tax as well. The way to validate the exemption is to attach a photocopy of the Form 1040NR to your state income tax return. That allows the state tax officials to see your reasoning for debiting your income by $5,000. Put $15,000 on the IT-203. Same logic applies to the NJ tax return as well.
Now, regarding payment of French taxes, the norm is that France would give you a credit for the U.S. taxes you paid, not the other way around. Most countries tax income earned within their borders, then the country of citizenship allows a credit. That's how the U.S. deals with income earned by its citizens in foreign countries. However, I have not researched U.S.-French Tax Treaty, so I am not familiar with its provisions.
Given your confusion, extensions may be in order for the federal and both states.
Further, this website (
http://www.thetaxguy.com) would be a better place to pose your questions, preferably directly to Dr. Carter. They may also be the best place to get professional help.