The showdown comes amid eurocrats demands to keep Northern Ireland under the rule of Brussels after the nation exits the bloc.
Mrs Foster told the EU chief there must not be an internal border within the UK and that they must not accept anything that will undermine the integrity of the union including England, Scotland, Wales and Northern Ireland.
Speaking during a press confrence after the meeting, Mrs Foster slated Mr Barnier’s proposed plans for the Irish border as “unacceptable”.
Mrs Foster said: “We feel the current draft EU legal text was not a faithful or fair translation of the joint report from December. We feel that the current draft legal text has omissions in it. It also overreaches in other areas.
“There are three options in relation to future relations, this has only reflected the third of those options, it doesn’t reflect the first and second. What’s the point of having a joint agreement if it’s not then later replicated into the document?”
The DUP wants to see a sensible Brexit which works for Northern Ireland, the United Kingdom but also for our nearest neighbours too
But she said Mr Barnier had been “receptive” of the DUP’s demands to find a “sensible” Brexit solution.
Mrs Foster added: “There will be a need to negotiate from that, we dont think its a fair interpretation and therefore work needs to be done.
“We are entering into negotiations around these isses and we wanted him to understand why we felt so strongly about the draft EU legal text as it stands.
“We have to work togetther to find solutions. We want to be pragmatic, make sure we have a sensible Brexit.”
Deputy leader Nigel Dodds said it was “ironic” for the EU to suggest setting up checks and a hard border between one part of UK and another part of the UK.
Arlene Foster will meet with Michel Barnier today
He said: “It is driving a coach and horses through the EU’s own principles about no hard borders.”
Mr Dodds then appeared to mock Mr Barnier by saying the EU chief had achieved a “great trick of bringing unity to the British parliament abd uniting parties on one part of Brexit was that the Conservative party, Labour Party under Keir Starmr and Emily Thornberry and ourselves had all come together to say that no Prime Minister could ever accept it”.
Mr Dodds added: “We told him he had achieved unity in Britain in terms of their approach to that.”
Speaking ahead of the meeting, Mrs Foster said she “stands ready to work for sensible solutions to the border question”.
Arlene Foster met with Barnier today
She said: “The DUP wants to see a sensible Brexit which works for Northern Ireland, the United Kingdom but also for our nearest neighbours too.
“We will not countenance any proposal which would create a new border in the Irish Sea between Northern Ireland and Great Britain.
“The economic and constitutional integrity of the United Kingdom must be respected and protected. Placing a border down the Irish Sea would not just be politically unacceptable but would be economically catastrophic.
DUP delegates meet Michel Barnier in Brussels
“A basis already exists to ensure people in Northern Ireland and the Republic can continue to work, move, and trade across the border freely after the UK has left the European Union. Greater flexibility needs to be shown by those in Brussels on the issue of the border.”
The DUP delegation will include Mrs Foster, her deputy Nigel Dodds, East Antrim MP Sammy Wilson and MEP Diane Dodds.
Prime Minister Theresa May has said “no prime minister could ever agree” to the EU’s draft treaty as she accused Brussels of attempting to “annexe” Northern Ireland.
The European Commission’s draft text for the UK’s withdrawal agreement sets out in legal terms plans for the establishment of a “common regulatory area” between the EU and Northern Ireland.
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The plans envisage an area spanning the whole island of Ireland with no internal borders and free movement of goods.
And it suggests that EU and UK customs authorities should jointly oversee movements between Northern Ireland and the British mainland, while Europe would retain control over aspects of taxation and state aid in the six counties.
But Mrs Foster is expected to tell EU bosses companies in Northern Ireland must have access to markets across the UK.
The meeting comes after Sinn Fein met with Michel Barnier after refusing to participate in three-way Brexit talks with the UK, Ireland and Brussels.