At the beginning of the all-island Brexit forum in Dundalk, County Louth, Mr Barnier said he knows that the so-called backstop has been the subject of "heated discussions in the UK". The UK has agreed in principle, but negotiators have been vague about how a seamless border would work.
"I don't think he does understand the wider unionist culture of Northern Ireland", Foster said.
Mr Barnier is on the second of a two day visit to Ireland and has spoken about his desire to avoid a hard border.
Mrs May has proposed policing the border with technology or creating a close economic partnership to render customs checks unnecessary, however, hardball European Union negotiators have rejected both plans and given Westminster till June to present an answer or sign off on their backstop.
Mr Barnier said that with the EU, Prime Minister Theresa May accepted the need to maintain an all island economy in Ireland, the peace process and the Good Friday Agreement in its entirety.
The EU chief negotiator was in the city to meet with business leaders.
"This is wrong", he told hundreds of audience at a local university in Dundalk, which also included Irish Prime Minister Leo Varadkar and Irish Foreign Minister Simon Coveney.
"I think it's political bad manners that the MEPs - and I have to saw the two council leaders from the DUP and UUP - were both invited here this morning and neither of them have turned up", she said.
The Irish border will be Britain's only land border when it leaves the union in March 2019 and it is one of the most hard challenges given the warring history between north and south.
He also rejected the Sinn Fein MEP's claim that he had snubbed Mr Barnier, adding that he meets the senior Brussels official on a regular basis.
GETTYEU leaders have driven a hard bargain over the Irish borderRelated articles You will notice that Northern Ireland is no longer in the European Union, and there will be consequences for that even if we have the backstop option.
"Ireland should also be lobbying for an arrangement to allow for a mutual recognition regime between the custom services of the United Kingdom and the EU".
The EU chief negotiator insisted today that he has "never been aggressive" during talks and stressed that his door is open to Mrs Foster and members of her party. "Now is the time to get Brussels to fully sign up", they write.
Brussels has not yet agreed to London's technological proposals to avoid a hard border, and Prime Minister Theresa May is under pressure at home and overseas to find a fresh solution.
"Until we reach this agreement and this operational solution for Northern Ireland, a backstop, and we are ready for any proposal...there is a risk, a real risk" he said.
"Whilst Mr Varadkar may say that he wants to find solutions to the issues facing us there is little demonstration of him working constructively to find them", he added.