"A signature is important, it reflects on the confidence the United Kingdom must continue to deserve by upholding its commitments," Michel Barnier told journalists in the Europresse association, according to AFP.
"Which is not what it's doing in Northern Ireland today, and which it is not doing with fishermen," he said.
He urged London to respect the Brexit terms on these two crucial issues "precisely as they were written in the two agreements of October 2019 and December 2020".
Tensions over fishing flared last week when French boats massed at the Channel Island of Jersey, claiming they were being denied licenses to fish off its shores despite a Brexit pledge of continued access.
British Navy vessels were sent in as were French patrol boats, and although the standoff ended it remains unclear if Jersey and Britain will apply new rules that Brussels has not endorsed.
"We have a serious problem concerning Jersey, which I don't understand, unless it's a question of unwillingness," Barnier said.
"There will probably be consequences."
The EU has already launched legal proceedings against Britain over a unilateral six-month delay to imposing customs controls on goods arriving in Northern Ireland from Britain.
The system is meant to prevent the return of a land border with Ireland, but effectively keeps Northern Ireland subject to EU rules on goods.