Nevertheless, Barnier said he was not rejecting the proposal outright.
Mr Barnier said they would be examining them in the light of three questions: "Is it a workable solution to avoid a hard border?"
Yesterday's agreement is created to provide a "backstop" - a guarantee of no hard border in Northern Ireland should other solutions fail.
Yesterday, Brexit secretary David Davis was, reportedly, threatening to resign over the wording of the government's proposal for a regulatory backstop if London and Brussels fail to strike a deal on the Irish border.
"There's a big prize for the United Kingdom here at the end of this and that prize is being able to be in control of our money, our laws and our borders, being more secure and more prosperous and being able to make those free trade deals with the rest of the world and a bright future".
"Best for Britain" said it was lobbying 70 MPs to "swing the Brexit debate" in parliament and wanted them to legislate in October to hold a referendum in March.
Davis has not commented directly on the source-based reports of his anger.
However, the document published on Thursday afternoon after Mrs May had her emergency meeting with Mr Davis and his allies, said that it expected a future deal to be in place by the end of 2021.More news: LeBron, Curry, Durant say National Basketball Association champ won't go to White House
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Shadow Brexit secretary Sir Keir Starmer described the PM's concession as "embarrassing".
Under the European Union proposal "Northern Ireland would form part of our customs territory", said Mr Barnier, adding: "What is feasible with a territory the size of Northern Ireland is not necessarily feasible with the whole United Kingdom".
"Instead, with the threat of a cabinet resignation, Theresa May has signed up to a flawed proposal which is inconsistent with her earlier commitments".
Mr Barnier said it would not be feasible to extend the European Commission's backstop plan - under which Northern Ireland would remain part of the EU's customs territory after Brexit - to include the whole of the UK.
Minister Theresa May unveiled a one-year "backstop plan" for the Irish border on Thursday.
"Victory for liberty! As I have been demanding for years, there must now be the same referendum in France and in all countries in the European Union", said Marine Le Pen, leader of France's right-wing Front National.
Prime Minister Theresa May declined to say Wednesday when the government would publish a promised document setting out its negotiating position.
Soros has angered some Brexit supporters who say he is seeking to undermine the outcome of the 2016 referendum which resulted in a 52-48 percent result in favour of leaving the EU.